# Maths_Quantitative_Aptitude by nuhman10

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QUANTITATIVE APTITUDE

(A) 4%                       (B) 5%
1. If a + b + c = 0, then (a3 + b3 + c3) ÷ abc is equal to:                1                            1
(A) 1                        (B) 2                                     (C) 6 %                      (D) 8 %
(C) 3                        (D) 9                                          4                            3
x 2 y 2 z2                                9. A sum of money at simple interest rate amounts to
2. If x + y + z = 0, then      +   +   is equal to:             Rs 4,025 in 3 years and to Rs 4,550 in 6 years at the same
yz xz xy
rate of interest. Find the sum and the rate of interest per
(A) 3                      (B) 27                                 annum.
(C) 1                      (D) –3                                      (A) Rs 2,500, 6%          (B) Rs 3,000, 5%
3. If ab + bc + ca = 0, then the value of                             (C) Rs 3,500, 5%          (D) Rs 4,500, 4%
1
+
1
+
1                                         10. In how many years, will a sum of Rs 800 at 10%
a2 – bc b2 – ca c2 – ab                                      per annum compound interest semi-annually become
Rs 926.10?
is equal to:                                                                      1                         1
(A) 3                      (B) 3 abc                                   (A) 2                     (B) 1
2                         2
(C) abc                    (D) 0
a       c is equal to:                               1                            1
4. If a + b = 2c, then      +                                        (C) 2                        (D) 1
a–c b–c                                               3                            3
(A) 2                         (B) 1                                    11. On a certain map of India the actual distance of
(C) 0                         (D) –2                              1450 kms between two cities Delhi and Kolkata is shown as
5. If x = a2 – bc, y = b2 – ca, z = c2 – ab, then the value      5 cms. What scale is used to draw the map?
(a + b + c)(x + y + z)                                                 (A) 1 : 15 × 106          (B) 1 : 20 × 106
of                          is:                                                             6
ax + by + cz                                                       (C) 1 : 25 × 10           (D) 1 : 29 × 106
12. The ratio between the third proportional of 12 and
(A) 3                       (B) 2                                  30 and mean proportional of 9 and 25 is:
(C) 1                       (D) 0                                       (A) 2 : 1                 (B) 5 : 1
6. The difference between compound interest and                        (C) 7 : 15                (D) 9 : 14
simple interest for 3 years at 5% per annum can be found                    13. 5 mangoes and 4 oranges cost as much as 3
out by multiplying the principal by:                                   mangoes and 7 oranges. What is the ratio of cost of one
(A) 1.7625                  (B) 0.7625                             mango to the cost of one orange?
(C) 0.07625                 (D) 0.007625                                (A) 4 : 3                 (B) 1 : 3
1                      (C) 3 : 2                 (D) 5 : 2
7. The simple interest on a sum of money is th
9                      14. Rs 1,050 are divided among P, Q and R. The share
of the sum and the number of years and the rate per                            2
of P is   of the combined share of Q and R. P gets:
cent per annum are equal. The rate per cent per annum                          5
is:                                                                         (A) Rs 320                   (B) Rs 300
1                                                                 (C) Rs 200                   (D) Rs 420
(A) 3                   (B) 5
3                                                                                              ma + nc
15. If a : b = c : d, then           is equal to:
2                                                                                           mb + nd
(C) 6                         (D) 10
3                                                             (A) an : mb                 (B) m : n
8. A man invested Rs 5,000 at some rate of simple                    (C) a : b                   (D) dm : cn
interest and Rs 4,000 at 1% higher rate of interest. If the                16. How many even numbers of four-digits can be
interest in both the cases after 4 years is same the rate of           formed with digits 1, 2, 3, 4, 5, 6 (repetition of the digit is
interest in the former case is:                                        allowed)?

528 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER
O B J E C T I V E -T Y P E Q U E S T I O N S

(A) 648                 (B) 180                                     hand is Rs 2,380, what is his salary?
(C) 1296                (D) 540                                         (A) Rs 5,000               (B) Rs 4,500
17. In how many ways 5 MBA students and 6 law                           (C) Rs 4,000               (D) Rs 3,500
students can be arranged together so that no two MBA
students are side by side?                                                    Directions (Q. Nos. 25 to 28): Read the following and
7!6!                                                           answer the questions that follow:
(A)                     (B) 6!.6!                                         Two friends Shyam and Kailash own two versions of a
2!
car. Shyam owns the diesel version while Kailash owns petrol
11
(C) 5!6!                   (D)        P5                            version. Kailash’s car gives an average that is 20% higher
than Shyam’s (in terms of litres per kilometre). It is known
18. There is a number lock with four rings. How many
that petrol costs 60% of its price higher than diesel.
attempts at the maximum would have to be made before
25. The ratio of cost per kilometre of Kailash’s car to
getting the right number?
Shyam’s car is:
(A) 104                     (B) 255
(A) 3 : 1                    (B) 1 : 3
(C) 104 – 1                 (D) 256
(C) 1.92 : 1                 (D) cannot be determined
19. There are four letters and four envelops addressed
26. Shyam’s car gives an average of 20 km per litre,
to different persons. In how many ways can wrong choices
then the difference in the cost of travel per kilometre between
the two cars is:
(A) 64                      (B) 23
(A) Rs 4.3                   (B) Rs 3.5
(C) 16                      (D) 255
(C) Rs 2.5                   (D) cannot be determined
20. There are 10 points on a straight line AB and 8
27. For the above question (26), the ratio of the costs
points on another AC, none of them being A. How many
per kilometre of the Shyam’s travel to Kailash’s travel is:
triangles can be formed with these points as vertices?
(A) 3 : 1                    (B) 1 : 3
(A) 720                     (B) 640
(C) 1 : 1.92                 (D) cannot be determined
(C) 816                     (D) 680
28. Diesel costs Rs 12.5 per litre, then the difference in
21. In a village consisting of p persons, x% can read
the cost of travel per kilometre between Kailash’s and
and write. Of the male alone y% and of the females alone 2%
Shyam’s is (assume an average of 20 km per litre for Shyam’s
can read and write. Find the number of males in the village
car and also assume that petrol is 50% of its own price higher
in terms of p, x, y and z, if z < y:
p(x – z)                  p(x – z)
than diesel):
(A)                        (B)                                            (A) Rs 1.75                  (B) Rs 0.875
( y + x – z)             ( y + x – 2z)
(C) Rs 1.25                  (D) None of these
p(y – x)                 p(x – z)                                 29. A shopkeeper gives 3 consecutive discounts of 10%,
(C)                        (D)                                      15% and 15% after which he sells his goods at a percentage
x–z                      y–z
profit of 30.05% on the cost price. Find the value of the
22. The price of a commodity is first increased by x%               percentage profit that the shopkeeper would have earned if
K                        he had given discounts of 10% and 15% only:
and then decreased by x%. If the new price is     , find the
100                             (A) 53%                      (B) 62.5%
original price from the given below:                                          (C) 72.5%                    (D) 68.6%
(x – 100)100               2     2                                  30. A journey of 192 kms takes 2 hours less by a fast
(A)                       (B) (x – 100 )100
K                        K                              train than by a slow train. If the average speed of the slow
train is 16 kmph less than that of a fast train, what is the
(x – 100)100                  100 K
(C)                        (D)                                      average speed of the fast train?
K                  (100 2 – x 2 )                           (A) 30 kmph                  (B) 48 kmph
23. A fraction is such that if the double of the                          (C) 20 kmph                  (D) 25 kmph
numerator and the triple of the denominator is changed by                     31. Two planes move along a circle of circumference
16                     1.2 kms with constant speeds. When they move in different
+ 10% and – 30% respectively, then we get 11% of     . Find
21                    directions, they meet every 15 seconds and when they move
in the same direction one plane overtakes the other every 60
fraction:
4                       2                                  seconds. Find the speed of the slower plane:
(A)                        (B)                                            (A) 0.04 km/s                (B) 0.03 km/s
25                       25
(C) 0.05 km/s                (D) 0.02 km/s
3                                                                32. The distance between two towns is x km. A car
(C)                        (D) None of these
25                                                          travelling between the towns covers the first ‘k’ km at an
24. A credits 15% of his salary in his fixed account and            average speed of y kmph and the remaining distance at z
spends 30% of the remaining on groceries. If the cash in                kmph. The time taken for the journey is:

529 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER
O B J E C T I V E -T Y P E Q U E S T I O N S

k (x – k )                                                     38. 2/3 of a consignment was sold at a profit of 6%
(A)     +
y    z                                                     and the rest at a loss of 3%. If, however, there was an overall
(k – x)                                               profit of Rs 540.00, the value of consignment was:
(B) ky +                                                             (A) Rs 1,620                   (B) Rs 4,860
z
(C) Rs 5,400                   (D) Rs 18,000
k k–x                                                                                                   1
(C)     +                                                            39. A cistern is filled by a tap in 3 hours. Due to a
y   z                                                                                                   2
(D) ky + z (x – k)                                                                              1
leak in its bottom, it takes     hour longer to fill. If cistern is
33. The metro service has a train going from Mumbai                                             2
to Pune and Pune to Mumbai every hour. The first one at 6
1                      full, how long will it take to leak to empty it?
a.m. The trip from one city to another takes 4 hours, and                  (A) 7 hours                (B) 8 hours
2
(C) 14 hours               (D) 28 hours
all trains travel at the same speed. How many trains will                  40. A can do a piece of work in 7 days of 9 hours each
pass while going from Mumbai to Pune, if you start at 12             whereas B can do the same work in 6 days of 7 hours each.
noon?                                                                How long will it take to complete the work together working
(A) 8                      (B) 10                                 2
8 hours a day?
(C) 9                      (D) 13                                 5
(A) 2 days                    (B) 3 days
Directions (Q. Nos. 34 to 38): Read the following and
1                             2
answer the questions that follow:                                         (C) 3 days                    (D) 4 days
A train journey from P to D by an X-express has 4 classes                 7                              5
of fares:                                                                 41. If 12 men and 16 boys can do a piece of work in 5
(i) 3 tier Rs 300       72 berths per       Train has           days and 13 men and 24 boys can do it in 4 days, the ratio
bogie               8 bogies            of daily work done by a man to that done by a boy is:
(ii) AC-3 tier Rs 898 64 berths per         Train has                (A) 1 : 3                   (B) 1 : 2
bogie               2 bogies                 (C) 2 : 1                   (D) 3 : 1
(iii) AC-2 tier         45 berths per       Train has                42. A bus left Delhi for Ambala at 50 km/hr and turned
Rs 1,388          bogie               2 bogies            over the same route at 40 km/hr. Thus it took 1 hour more
(iv) AC-first class     26 berths per       Train has           on the return trip. The distance between Delhi and Ambala
Rs 2,691          bogie               one bogie
is:
The distance between P to D is 1100 km. Assume the
(A) 200 kms
train does not stop at any station unless otherwise indicated.
(B) 180 kms
The running cost per kilometre : AC-bogie—Rs 25, non-AC-
(C) 400 kms
bogie—Rs 10.
(D) None of these
34. Assuming full occupancy, a bogie of which class
43. A train running at 72 kms per hour crosses a
exhibits the highest profit margin?
coconut tree standing by the side of the track in 7 seconds.
(A) AC-3 tier                (B) AC-2 tier
The length of the train is:
(C) AC-first class           (D) 3 tier
(A) 104 metres
35. Assuming full occupancy in all the classes, for a
(B) 140 metres
journey between P and D to Delhi, the profit margin (as a
(C) 504 metres
percentage of running costs) of the class showing the lowest
(D) 540 metres
profit is approximately:
44. A man purchased a bag of rice containing 70 kgs
(A) 116%                     (B) 127%
for Rs 175. He sold it at the rate of Rs 2.75 per kg. Find the
(C) 109%                     (D) None of these                  profit and loss per cent.
36. For the above question, the percentage of the total              (A) 10% profit              (B) 10% loss
profit that comes out of AC bogie is (approximately):                     (C) 12.5% profit            (D) 12.5% loss
(A) 50%                      (B) 60%                                 45. If 16% of 140% of a number is 28, the number is:
(C) 70%                      (D) 80%                                 (A) 200                     (B) 225
37. The highest revenue for a journey from P to D will               (C) 125                     (D) 320
always be generated by:                                                   46. A person marks his goods 20% higher than the
(A) 3 tier                                                      cost price and allows a discount of 5%. The percentage of
(B) AC-3 tier                                                   profit is:
(C) AC-2 tier                                                        (A) 15%                     (B) 20%
(D) cannot be determined                                             (C) 5%                      (D) 14%

530 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER
O B J E C T I V E -T Y P E Q U E S T I O N S

1. (C) Q a + b + c = 0 ∴ a3 + b3 + c3 = 3 abc                                                           A=P+I
or (a3 + b3 + c3) ÷ abc = 3                                                                      ∴ P = 4025 – 525 = Rs 3500
x2 y2 z2   x 3 + y 3 + z 3 3xyz                                                                  525 × 100
2. (A)      +  +   =                =     =3                                                            R=           =5
yz xz xy        xyz         xyz                                                                   3 × 3500
10
(Q x + y + z = 0)                                                                                            1
10. (B) 926.10 = 800 (1 + 2 )n ⇒ n = 3 half years = 1 years
3. (D) ab + bc + ca = 0 ⇒ bc = – (ab + ca)                                                                             100                         2
ca = – (ab + bc)                                                     11. (D)
ab = – (bc + ca)
302
Given exp                                                                              12. (B) Third proportional of 12 and 30 =         = 75
1               1                1                                                                                    12
=                     +               +
a 2 – bc             b 2 – ca        c 2 – ab                                             Mean proportional of 9 and 25 =     9 × 25 = 15
1                        1                  1                                                75 5
=                              +                           +                                      Reqd ratio =     = =5:1
a + ca + ab
2
b + ab + bc c + bc + ca
2           2                                                               15 1
1                1               1                                        13. (C) Let the cost of 1 mango be Rs x and that of 1 orange
=                     +                +                                                        be Rs y
a ( a + c + b)   b ( b + a + c ) c ( c + b + a)
x 3
bc + ca + ab          0                                                                     ATS 5x + 4y = 3x + 7y ⇒    =
=                =                =0                                                                                     y 2
abc(a + b + c)   abc(a + b + c)
14. (B) Let the combined share of Q and R be Rs x
4. (B) a + b = 2c or a – c = c – b = – (b – c)                                                            2x
a       c         a         c                                                                ∴      + x = Rs 1050 ⇒ x = 750
+       =          +                                                                          5
a – c b – c –( b – c) b – c
2
–a + c –(a – c) b – c                                             ∴ Share of P =     × 750 = Rs 300
=       =        =      =1                                                           5
b–c     b–c      b–c
a c
(a + b + c)(x + y + z)                                                       15. (C)     = = k ⇒ a = bk, c = dk
5. (C)                                                                                                   b d
a(a2 – bc) + b(b2 – ca) + c(c2 – ab)
ma + nc     mbk + ndk
=                =k=a:b
(a + b + c)(x + y + z)                                                  mb + nd        nb + nd
=
a 3 – abc + b 3 – abc + c 3 – abc                                        16. (A) Unit’s place be filled in 3 ways (i.e. by 2 or 4 or 6)
(a + b + c)(x + y + z)                                                           Each of three remaining places (i.e. ten’s hundred’s
=
a 3 + b 3 + c 3 – 3abc                                                          and thousand’s) can be filled in 6 ways
(Q repetition is allowed)
(a + b + c)(a 2 – bc + b 2 – ca + c 2 – ab)                                         ∴ Reqd. no. of nos. = 6 × 6 × 6 × 3 = 648
=
a 3 + b 3 + c 3 – 3abc                                     17. (A) 6 law students can be arranged in 6! ways
a3 + b3 + c3 – 3abc = 1                                                              Now in 7 places, 5 MBA students can be arranged
=                                                                                           in 7P5 ways .× . × . × . × . × . × .
a3 + b3 + c3 – 3abc                                                                                                       6! × 7 !
∴ Total no. of ways = 6! × P5 =
7

6. (D) P
LMFG1 + R IJ n – 1OP – P × R × T                                                                                             2!

NMH 100K QP 100                                                             18. (C)
19. (D) 44 – 1 = 255
LMRF 5 I
|                 3        U
|   5×3     OP                                 20. (B) 8C2 × 10 + 10C2 × 8 = 640
=P       MNSGH1 + 100 JK
|
T
–1 – V
|
W   100 = P × .007625
PQ                                               [No. of bases on AC = 8C2
No. of vertices on AB = 10
s
∴ No. of ∆ with bases on AC and vertices
P P× R× R              10     1
7. (A)    =            ⇒ R=       =3                                                                                    8
on AB = C2 × 10
9       100             3     3                                                                                s
No. of ∆ with bases on AB and vertices
4                    4
8. (A) 5000 × x ×       = 4000 (x + 1) ×     ⇒ x=4                                                            on AC = 10C2 × 8]
100                  100                                                                                                 px
9. (C) I for 3 years = Rs 4550 – 4025 = Rs 525                                                21. (D) Total persons who can read and write =
100

531 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER
O B J E C T I V E -T Y P E Q U E S T I O N S

Let the no. of males be M                                        34.   (D)   3 tier
y             z   px                                 35.   (D)
A.T.S. M×      + (p – M)    =
100           100 100                                 36.   (B)   60%
p(x – z)                                                     37.   (A)   3 tier
⇒ M = y–z                                                         38.   (D)   Let total value of consignment be Rs x
2     106 x 97
A.T.S. x ×         + ×      – x = 540
22. (D) Let the original price be Rs y                                                          3     100 3 100
y
FG 100 + x IJ FG 100 – x IJ = k ⇒ y = 100k                               ⇒ x = Rs 18000
H 100 K H 100 K 100                 100 – x  2   2
2
x                                               39. (D) Tap’s 1 hour’s work =
23. (B) Let the fraction be                                                                                      7
y
Let the reqd time be x hrs
110                                                            2 1 1
2x ×                                                          ATS – = ⇒ x = 28
A.T.S.      100 = 11 × 16 ⇒ x = 2                                          7 x 4
70   100 21    y 25                                                                1
3y ×
100                                              40. (B) A’s one day’s work =         (by working 1 hour a day)
63
24. (C) Let his salary be Rs x                                                                                     1    1     5
85x 70                                                                    (A + B)’s one day’s work =   +     =
A.T.S.      ×      = 2380 ⇒ x = Rs 4000                                                                    63 42 126
100 100
42
25.   (C)                                                                               (A + B)’s work by working    hours a day
5
26.   (D)
5 42 1
27.   (C)                                                                                                                 =      × =
28.   (D)                                                                                                                     126 5 3
29.   (A) Let CP = Rs 100, P = 30.05%                                                   Reqd time = 3 days
∴ S.P. = Rs 130.05
41. (C) Work done by 12 M + 16B in 5 days
Discounts = 10%, 15%, 15%
= work done by 13 M + 24 B in 4 days
100 100 100
∴ M.P. = 130.05 ×    ×     ×  = Rs 200                                    ⇒ 60M + 80B = 52 M + 96 B ⇒ 1M = 2B
90 85 85
M 2
If discounts are 10% and 15% only                                           =        2 : 1 = Reqd ratio
B   1
∴ S.P. = M.P. ×
FG 100 – d IJ × FG 100 – d IJ
1               2
D D
H 100 K H 100 K                               42. (A)        –
40 50
= 1 ⇒ D = 200 km
90   85
= 200 ×       ×    = Rs 153                              43. (B) Let the length of train be x
100 100
x
∴                 = 7 ⇒ x = 140 m
∴ Profit = 53%                                                                         5
72 ×
192     192                                                                          18
30. (B)           –     = 2 ⇒ x = Speed of fast train = 48
x – 16    x
44. (A) C.P. of 70 kg rice = Rs 175
31. (C) Let the speeds of fast plane and slow planes be x                                              385
S.P. = 2.75 × 70 =
and y m/sec respectively             D=s×t                                                      2
If they move in opposite direction
385          35
15 (x + y) = 1200 ⇒ x + y = 80 m/sec           ... (i)                           P= – 175 =
2            2
If they move in same direction, relative speed
= x – y m/sec                                                                      35     1
∴ P% =    ×        × 100 = 10
Time = 60 i.e. 4 times                                                             2     175
1                                                                    16 140
∴ Speed is 4 th x – y = 20 m/sec              ... (ii)                45. (C)        ×    × x = 28 ⇒ x = 125
100 100
Solving (i) and (ii),                                                 46. (D) Let CP = Rs 100
y = 50 m/sec = 0.05 km/sec                                                   ∴ MP = Rs 120
k     x–k                                                                   95
32. (A) Reqd time =       +                                                         S.P. = 120 ×     = Rs 114
y      z                                                                   100
33. (D) 13 trains                                                                       ∴ P% = 14

532 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER

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