GRE PAPER- V
1. DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. 72 < 5x < 86 Column A Column B x 16 (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given
⇒ 72 86
Solution 2.
(d) Given 72 < 5x < 86
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. The ratio of C.P. and S.P. is 4 : 5. Column A Column B % Profit 25% (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given (c) Column A : Profit = 5x – 4x = $x x × 100 = 25% 4x % Profit = Let C.P. = $ 4x and S.P. = $5x
Solution
3.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. An ore contains 5% of aluminium. To get 52 kg of aluminium, the quantity of ore is x kg. Column A Column B x 1050 (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given
Quantity of ore Quantity of Al (in kg.) (in kg.) 5 100 52 x Solution. (b)
It's direct proportion. ⇒ 100 : x : : 5 : 52 ⇒ 5 × x = 100 × 52 ⇒ x =
100 × 52 = 1040 Kg. 5
4.
In the figure below, if ∠ABC = 35°, then the value of ∠ACB is equal to
P
A
Q
B
35° O
C
D
(a) 55° (e) 65º Solution (b) 50° (c) 45° (d) 54°
(a) ∠BAC = 90º Now, ∠BAC + ∠ABC + ∠ACB = 180º ⇒ ∠ACB = 180º – 90º – 35º = 55º
2x − 5 5x − 2 2x − 5 2x + 5
[Angle in the semicircle]
5.
Which of the following functions y = f(x) is such that x = f(y)?
y= y= y=
(a) (e)
(b)
(c)
−2 x − 5 5x − 5
y=
(d)
2x + 5 2 − 5x
3x + 5 y= 5 − 3x ax − b
Solution. 6.
(a) For any function y = f(x) of the type y = bx − a has x = f(y).
The length of a rope by which a horse must be tethered so that it may be allowed to graze over an area of 784 square metres is (a) 18.44 m (b) 13.69 m (c) 15.8 m (d) 22.31m (e) 16.81 m (c) π r2 = 784 ⇒ r = 15.8 m = length of rope.
Solution. 7.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. The ratio of milk and water in a mixture is 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. Column A Column B The quantity of milk in the given mixture 8 litres (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given
Solution. (a) Let the quantity of milk in mixture = 4x litres and let the water in mixture = 3x litres.
4x 4 5 = ⇒ 20x = 12x + 20 ⇒ 8x = 20 ⇒ x = . 3x + 5 5 2 Now,
Column A : The quantity of milk in the given mixture = 4 ×
5 2
= 10 litres.
8.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. Column A Column B The product of odd integers from –5 to 5 0 (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given Column A : Integers are –5, –3, –1, 1, 3, 5. Therefore, their product is always negative because the number of negative terms is odd.
Solution. (b)
9.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. Column A Column B 91 + 191 + 591 101 + 251 + 521 (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given
Solution. (c) Column A : 91 + 191 + 591 = 873; Column B : 101 + 251 + 521 = 873. Directions for questions 10 and 11 : The bar-graph given below shows the percentage distribution of total expenditures of a Company under various expense heads during 2003. Study the graph and answer the questions that follow : PERCENTAGE DISTRIBUTION OF TOTAL EXPENDITURE OF A COMPANY
25 Percent Spent 20 15 10 5 Infrastructure 0 Advertisement Transport Taxes 20 12.5 15 10 5 Research and Development Salary 20 17.5
10.
The total amount of expenditure of the Company is how many times the expenditure on research and development? (a) 27 (b) 20 (c) 18 (d) 8 (e) 5 (b) Let the total expenditure be $x
⎛ x ⎞ ⎜ ⎟ Then, the expenditure on Research and Development = (5% of x) = $ ⎝ 20 ⎠
Solution.
x 20 = x ⎞ 1 ⎛ ⎜ ⎟ Ratio of the total expenditure to the expenditure on Research and Development ⎝ 20 ⎠
=. Thus, the total expenditure is 20 times the expenditure on Research and Development.
Interest on Loans
11.
If the interest on loans amounted to 2.45 million dollars, then the total amount of expenditure on advertisement, taxes and research and development is : (a) 7 million dollars (b) 5.4 million dollars (c) 4.2 million dollars (d) 3 million dollars (e) 2.4 million dollars (c) Let the total expenditure be x million dollars Now, 17.5% of x = 2.45 x = 14 Total expenditure = 14 million dollars Thus, the total expenditure on advertisement, taxes and research and development = [(15 + 10 + 5)% of 14] million dollars = (30% of 14) million dollars = 4.2 million dollars.
Solution.
12.
In the figure below, if PQR is an isosceles triangle and PSR is an equilateral triangle and X = 26° then the value of Y (in degrees) will be
Q X
S Y P
(a) 17° (e) None of these. Solution. (b) 27° (c) 37°
R
(d) 47°
(a) We have, PQ = QR ⇒ ∠QPR = ∠QRP Now,
∠PQR + ∠QPR + ∠QRP = 180° ⇒ ∠PQR + 2∠QPR = 180° ⇒ 26° + 2( y + 60°) = 180°
⇒ 2 y = 180° − 120° − 26° = 34° ⇒ y = 17°.
13.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. Column A Column B 21 × 35 27 × 32 (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given Column A : 21 × 35 = 735; Column B : 27 × 32 = 864.
Solution. (b) 14.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer.
D 3 O 1 A
C
6
B
Column A Column B Area of ΔOBD 6 (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given Solution. (a) Column A : For ΔOAB, height = 6 unit, base = 3 unit.
1 × base × height = 9 sq. unit
∴ Area of ΔOAB = 2 15.
If 2x+1 × 28 = 32x × 16, then the value of x is (a)
1 3
(b)
2 5
(c) 2
x +1+8
5 4
(d)
5 4
Solution.
x +1 8 x (d) 2 × 2 = 32 × 16
or 2
= 25x 2 4 or 2 x +9 = 25x + 4
5x + 4 = x + 9 or 4x = 5 or x = 16.
A train is going from Johannesburg to Pretoria stops at nine intermediate stations. Six persons enter the train during the journey with six different tickets. How many different sets of tickets may they have had?
C6 (a) (e) None of these
55
(b)
45
C6
(c)
54
C6
(d)
9C 2
Solution.
(a) Johannesburg to Pretoria = 9 stations Total number of stations = 11
11
2 Total no. of different sets of tickets printed = Thus six persons would have 55C6 different sets of tickets.
C2 =
11× 10
= 55
17.
The average of first five multiples of 3 is: (a) 3 (b) 9 (e) 8
3(1 + 2 + 3 + 4 + 5) 45 5 = 5 =9 (b) Average =
(c) 12
(d) 15
Solution. 18.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. In 10 years, A will be twice as old as B was 10 years ago. A is now 9 years older than B. Column A Column B The present age of B 40 (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given Column A : Let present age of B = x years and present age of A = (x + 9) years Given : (x + 9) + 10 = 2 (x – 10) ⇒ x + 19 = 2x – 20 ⇒ x = 39 years.
Solution. (b)
19.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer.
C
x y 40°
D
A
B AB || CD
Column A Column B x + y + 40 100 (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given Solution. (a) Column A :
∠y = ∠x = 40° (opposite angle) ∴ x + y + 40 = 40 + 40 + 40 = 120° .
∠x = 40° (corresponding angle)
20.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. x – 4 = 11 Column A Column B 112 x2 – 4 (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given
Solution. (a) Given : x – 4 = 11 ⇒ x = 15. Column A : x2 – 4 = (15)2 – 4 = 225 – 4 = 221. Column B : 112 = 11 × 11 = 121. 21. There are 5 red shoes and 4 black shoes in a bag. They have got all mixed up. Find the probability of getting a correct pair of shoes, if two shoes are drawn at random. (a) (e) Solution.
2 3
(b)
4 9
(c)
2 9
(d)
5 9
4 13
(b) Required probability = Prob.(both are red) + Prob.(both are black)
=
5 9
C2 C2
+
4 9
C2 C2
=
5× 4 4× 3 8 4 + = = 9 × 8 9 × 8 18 9
22.
In the figure below, if BD || EF, then is
A
E
F
40° B
(a) 100° (e) 110º Solution. 23. (b) 120°
C
(c) 140°
D
(d) 160°
(c) ∠DCE + ∠CEF = 180° ⇒ ∠CEF = 180° − 40° = 140°.
If 16% of 40% of a number is 8, then the number is, (a) 200 (b) 225 (c) 125 (e) 512 (c) Let the number be x.
x.
(d) 325
Solution.
Now, 24.
40 16 8x . = 8 or = 8 or x = 125. 100 100 125
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer. If selling price is doubled, the profit triples. Column A Column B % Profit 100% (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given
Solution. (c) Let Selling price = x, Cost price = y then Profit = x – y Given : (2x – y) = 3 (x – y) ⇒ x = 2y Profit = 2y – y = y.
⎛y ⎞ % Profit = ⎜ × 100⎟% = 100% ⎜y ⎟ ⎝ ⎠ Column A :
25.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, .you are to compare the two quantities and then give the answer. A box contains 10 black and 10 white balls. Column A Column B
8 19 The probability of drawing two balls of same colour (a) quantity in column A is greater (b) quantity in column B is greater (c) both quantities are equal (d) the relationship cannot be determined from the information given
Solution. (a) n(S) = 20C2, n(E1) = 10C2, n(E2) = 10C2 Required probability =
n ( E1 ) n ( E 2 ) + = n (S) n (S)
10 20
C2 C2
+
10 20
C2 C2
=
9 9 18 9 + = = 38 38 38 19
26.
DIRECTIONS: The question consists of two quantities. One in Column A and one in Column B, you are to compare the two quantities and then give the answer.
B x° O A
In the figure, the ratio of length of arc AB to the circumference of circle is 2: 9. Column A Column B (a) (b) (c) (d)
∠x 100 quantity in column A is greater quantity in column B is greater both quantities are equal the relationship cannot be determined from the information given
2πr x 360
Solution. (b) Column A : Since length of arc AB =
2πr. x 360 = 2 ⇒ x = 360 × 2 = 80° 2πr 9 9
Given :
Directions for questions 27 and 28 : Study the following graph carefully and answer the questions that follow : The following graph shows the passenger car per 1000 people and accidents per 1000 motor vehicles.
Passenger cars (per 1000 people) Accident (per 1000 motor vehicles) 61 600 500 400 300 12 200 100 5 0 Germany S. Korea US Countries India Indonesia UK 12 1 163 33 16 13 506 483 375
70 60 50 40 30 20 10 0
27.
Total motor vehicle accidents in UK is what times of that of passenger cars in Germany? (a) 83.43% (b) 38.92% (c) 1.34% (d) Data inadequate (e) None of these
Solution. 28.
(d) Absolute value of neither is given.
What is the ratio of total passenger cars per thousand and the total motor vehicle accidents per thousand of all the given countries? (a) 17 : 193 (b) 15 : 1 (c) 193 : 17 (d) 1 : 15 (e) None of these (c) Total passenger cars per thousand = 506 + 163 + 483 + 5 + 12 + 375 = 1544 Total motor vehicle accidents per thousand = 12 + 33 + 16 + 61 + 1 + 13 = 136 Required ratio = 1544: 136 = 193: 17.
Solution.