divelab/Sys2Bench huggingface dataset:
Question: A pipe can fill a cistern in 7 minutes whereas the cistern when fill can be emptied by a leak in 14 minutes. When both pipes are opened, find when the cistern will be full?
Options:
A)17
B)16
C)70
D)14
E)12
Rationale: 1/7 - 1/14 = 1/14
14 minutes
Answer: D
Answer: D
Question: Due to an increase in 30% in the price of eggs, 3 eggs less are available for Rs. 7.80. Find the present rate of eggs per dozen.
Options:
A)Rs. 9.36
B)Rs. 10.36
C)Rs. 11.36
D)Rs. 12.36
E)Rs. 14.36
Rationale: Explanation:
Let the original price per egg be Rs x
Then increased price will be,
(130/100)x
=>7.80/x- 7.80/ 130/100x =3
=>x=0.6
Actual price was Rs 0.6,
Present price per dozen will be
Rs.(12*130/100*0.6)=Rs.9.36
(130100x)=>7.80xâˆ’7.80130100x=3=>7.80xâˆ’780130x=3=>390x=234=>x=0.6Actual price was Rs 0.6Present price per dozen will beRs.(12âˆ—130100âˆ—0.6)=Rs.9.36
ANSWER IS A
Answer: A
Question: If the average (arithmetic mean) of three consecutive integers is 21, then the product of the greatest and least integer is
Options:
A)443
B)442
C)440
D)444
E)441
Rationale: n = smallest number
n+2 = largest number
(n + n + 2)/2 = 21
=> (2n+2)/2 = 21
=> n + 1 = 21
=> n = 20
So Product of n and n+2 = (20)(22)
= 440
Answer - C
Answer: C
Question: In expressing a length 81.469 km as nearly as possible with three significant digits, find the percentage error?
Options:
A)0.075%
B)0.156%
C)0.034%
D)0.038%
E)0.152%
Rationale: Error = 81.5-81.469 = 0.031
Required percentage = (0.031/81.469)*100 = 0.038%
Answer is D
Answer: D
Question: In how many ways can the letters of the word BUTTER be arranged in a row so that the vowels appear in alphabetic order?
Options:
A)380
B)420
C)360
D)400
E)320
Rationale: two letters can be arranged in 2! ways.
only one combination EU is required.
6 letters can be arranged in 6! ways.
thus 6!/ 2! * 1 = 360
C
Answer: C
Question: If there are 4 seats and two students, in how many ways can they be seated?
Options:
A)12
B)6
C)8
D)16
E)10
Rationale: No. of ways of choosing 2 chairs out of 4 chairs on which two students will sit = 4C2 = 6
No. of ways of 2 people sitting on selected chairs = 2!
Total ways of making 2 people sit on 2 of 4 chairs = 4C2*2! = 6*2 = 12
ANSWER:A
Answer: A
Question: The greatest number that divides 3560 and 3450 leaving remainder 4 and 6 respectively is:
Options:
A)23
B)25
C)26
D)28
E)30
Rationale: explanation:
3560-4=3556 ,3450-6=3444
Highest number that can divide 3556 and 3444 is HCF of numbers
HCF of 3556 and 3444 =28
Answer :D
Answer: D
Question: If '+' denotes ÷ , '–' denotes ×, ‘×’ denotes – and ‘÷’ denotes +, then
35 + 7 – 5 ¸5 × 6 = ?
Options:
A)22
B)26
C)24
D)28
E)29
Rationale: C
24
35÷ 7 × 5 + 5 – 6
= 5 × 5 + 5 – 6
25 + 5 – 6
30 – 6 = 24
Answer: C
Question: A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)50 sec
C)44 sec
D)49 sec
E)60 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer:C
Answer: C
Question: The average age of 9 men increases by 4 years when two women are included in place of two men of ages 36 and 32 years. Find the average age of the women?
Options:
A)78
B)26
C)52
D)54
E)56
Rationale: Explanation:
36 + 32 + 9 * 4 = 104/2 = 52
Answer: C
Answer: C
Question: Excluding stoppages, the speed of a bus is 52 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options:
A)7 min
B)6 min
C)9 min
D)8 min
E)11 min
Rationale: Due to stoppages, it covers 7 km less.
Time taken to cover 7 km =(7/52)x60 = 8 min
answer : D
Answer: D
Question: A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement?
Options:
A)1850
B)2960
C)3000
D)1110
E)1712
Rationale: 1850 ---- 28
1850 ---- 16
x ----- 10
x*10 = 1850*16
x = 2960
1850
-------
1110
Answer: D
Answer: D
Question: The Hat Company makes hats of different colors, some plain and some with printing. For a particular order of hats, 2 out of every 3 hats are blue. If 1 out of every 3 blue hats has printing, and there are 200 blue hats with printing in the shipment, how many hats total are there in the shipment?
Options:
A)200
B)900
C)1,000
D)5,000
E)520
Rationale: Proportions: Let H = hats, and Hb = blue hats, and Hbp = blue hats with printing.
200Hbp/xHb = 1Hbp/3Hb
xHb = 600Hb
600Hb/yH = 2Hb/3H
yH = 900H
Answer: B
Answer: B
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 30km/hr, then find the area of square field.
Options:
A)125
B)225
C)325
D)425
E)None of these
Rationale: Explanation :
D = 30*3/2 = 45 km. So side of square is 22.5km, so area – 506.25km^2
Answer – E
Answer: E
Question: A cistern 6m long and 5 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Options:
A)49 m2
B)50 m2
C)53.5 m2
D)55 m2
E)57.5 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (5 x 1.25 + 6 x 1.25) + 6 x 5] m2
= 57.5 m2.
Answer: Option E
Answer: E
Question: A rectangular cube has a volume of 7 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Choices
Options:
A)24
B)48
C)56
D)80
E)100
Rationale: Lets say the sides of the rectangular cube are x, y and z. Problem states volume is 7.
i.e,
x*y*z = 7 .
If every side is increased twice as before. then new volume is
2x*2y*2z = 8*(x*y*z) = 8*7 = 56.
Answer is C
Answer: C
Question: If d=1/(2^3*5^9) is expressed as a terminating decimal, how many nonzero digits will d have?
Options:
A)One
B)Two
C)Three
D)Seven
E)Ten
Rationale: Another way to do it is :
We know x^a*y^a=(X*Y)^a
given = 1/(2^3*5^9)
= Multiply and divide by 2^4
=2^6/(2^3*2^6*5^9)
=2^6/10^9
=> non zero digits are 64 => Ans B
Answer: B
Question: If the side of a square is increased by 55%, its area is increased by?
Options:
A)140%
B)145%
C)150%
D)160%
E)none of these
Rationale: Since Side x Side = Area
Therefore, net% change in area
= ( x + y + xy/100) %
= [55 + 55 + (55 x 55)/100]% or 140.25%
Therefore, area is increased by 140.25%
ANSWER:A
Answer: A
Question: The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 15 consecutive integers that start with (m + 2)?
Options:
A)m + 4
B)n + 6
C)n + 7
D)m + 5
E)n + 4
Rationale: The average of consecutive numbers is the middle number.
Then n = m+2.
The average of 15 consecutive numbers starting from n is n+7.
The answer is C.
Answer: C
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,055. How much did she invest at 5%?
Options:
A)$500
B)$600
C)$700
D)$900
E)$950
Rationale: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1055/1000)-1 = 0.055 = 5.5%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.055
(0.05)x +0.06 - (0.06)x = 0.055
-0.01x = -0.005
x= -0.005/-0.01 = 5/10 = 50%
So X = 50% of the 1000 which is 500
ANSWER:A
Answer: A
Question: What is the perimeter of a square field whose diagonal is 8âˆš2?
Options:
A)64 m
B)32 m
C)30 m
D)16 m
E)18 m
Rationale: Explanation:
aâˆš2=bâˆš2 ->a=8
4a = 32 m
ANSWER IS B
Answer: B
Question: The product of the squares of two positive integers is 1600. How many pairs of positive integers satisfy this condition?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Ans: E - 4 pairs
(xˆ2)(yˆ2) = 1600 [square root both sides]
xy = 40
40 = 1x40, 4x10, 40x1, 10x4, 5x8, 8x5, 20x2, 2x20
Cancel the repeats
This leaves us with exactly 4 options.
Hence, E
Answer: E
Question: The sum of first five prime numbers is:
Options:
A)28
B)29
C)24
D)22
E)43
Rationale: A
28
Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
Answer: A
Question: Find the fourth proportional to 5.1, 3.6 and 2.3?
Options:
A)2.62
B)1.22
C)3.12
D)2.62
E)1.62
Rationale: Explanation:
Formula = Fourth propotional = (b × c)/a
A = 5.1 , B = 3.6 and C = 2.3
(3.6 × 2.3)/5.1 = 1.62
Answer: Option E
Answer: E
Question: In a workshop there are 4 kinds of beds, 3 kinds of closets, 3 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
Options:
A)A)168.
B)B)80.
C)C)56.
D)D)48.
E)E)120.
Rationale: ways to select one shelf = 3
ways to select one bed = 4
ways to select one of the following: a chair or a closet = 7+3 = 10
ways to select all of them together = 3*4*10 = 120
Answer : E
Answer: E
Question: ((1^7m)/(5^7m))((1^18)/(4^18)) = 1/(2(10)^35)
What is m?
Options:
A)17
B)5
C)34
D)35
E)36
Rationale: ((1^7m)/(5^7m))((1^18)/(4^18)) = 1/(2(10)^35)
((1/5)^7m ) * ((1/2)^36) = 1/ (2 * (2*5)^35))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^7m= (1/5)^35
((1/5)^7m ) * ((1/2)^36) = 1/[(2^36)*(5^35)]
So, m=5
ANswer B
Answer: B
Question: If b < 2 and 4x - 8b = 0, which of the following must be true?
Options:
A)x > -3
B)x < 5
C)x = 4
D)x < 4
E)D. x > 3
Rationale: 4x - 8b = 0
Therefore, 4x = 8b
As, b<2
4x < 8(2)
i.e x < 4
Answer : D
Answer: D
Question: David is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 3 miles per hour and returns along the same route at an average speed of 8 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
Options:
A) 4.3
B) 5.8
C) 6.0
D) 6.3
E) 6.5
Rationale: to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here David's uphill speed = 3 mph
David's downhill speed = 8 mph
2*3*8/(3+8) = 48/11 = 4.3
Correct answer - A
Answer: A
Question: A boat goes 100 km downstream in 10 hours, and 90 km upstream in 15 hours. The speed of the stream is?
Options:
A)5km/h
B)4km/h
C)2km/h
D)(1/2) km/h
E)E)None
Rationale: 100 --- 10 DS = 10
? ---- 1
90 ---- 15 US = 6
? ----- 1 S = (10 - 6)/2
= 2 kmph
ANSWER:C
Answer: C
Question: Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different.
Options:
A)z=3x
B)x=3z
C)y=2x
D)x=2y
E)y=3x
Rationale: Rovert Travelled for x,y and for z min.
Total Time : x + y + z
Which is equal to : 3y
Equating both sides we get
x+y+z = 3y
=> x+z =2y ........ Eqn 1
Looking out at options
D Says x =2y
Using it in Eqn 1
2y + z = 2y
=> Z = 0 mins, Which I guess is not possible.
The Ans isD
Answer: D
Question: (1/2) of a number is 3 more than the (1/6) of the same number?
Options:
A)6
B)7
C)8
D)9
E)5
Rationale: let number is=x;
by question-------
x/2=(x/6)+3
x/2-x/6=3
x=9
ANSWER:D
Answer: D
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 20 cm2. Find the lengths of all sides.
Options:
A)10 and 3
B)7 and 10
C)11 and 8
D)3 and 10
E)10 and 10
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 20 cm2 more than the first area. Therefore
A1+20=A2
x(x−3)+20=(x+1)(x−2)
x2−3x+20=x2+x−2x−2
2x=22
x=11. So, the sides of the rectangle are 11 cm and (11−3)=8 cm long.
So answer is C.
Answer: C
Question: What will be the remainder when 17^200 is divided by 18 ?
Options:
A)3
B)8
C)5
D)1
E)7
Rationale: When n is even,(x^n-a^n) is completely divisible by (x-a).
(17^200-1^200)is completely divisible by (17+1),
(17^200-1) is completely divisible by 18.
On dividing 17^200 by 18,we get 1 as remainder.
Answer is D
Answer: D
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 108 grams of water?
Options:
A) 16
B) 96
C) 112
D) 128
E) 142
Rationale: Solution:
We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 108 grams of water.
2x + 16x = 108
18x = 108
x = 6
Since x is 6, we know that there are 16 x 6 = 96 grams of oxygen in 108 grams of water.
Answer B.
Answer: B
Question: In a staircase, there ar 10 steps. A child is attempting to climb the staircase. Each time she can either make 1 step or 2 steps. In how many different ways can she climb the staricase?
Options:
A)23
B)277
C)18
D)178
E)181
Rationale: Use fibonnacci series, with starting two terms as 1, 2. So next terms are 3, 5, 8, 13, 21, 34, 55, 89
Answer:B
Answer: B
Question: If 1.5 cm of a pencil is purple, 0.5 cm of the remaining is black and the remaining 2 cm is blue, what is the total length of the pencil?
Options:
A)5 cm
B)3 cm
C)1 cm
D)4 cm
E)2 cm
Rationale: Purple is 1.5 cmBlack is 0.5 cmBlue is 2 cm1.5+0.5+2=4 cmAnswer is D) 4 cm
Answer: D
Question: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
Options:
A)28
B)25
C)27
D)23
E)21
Rationale: Let the pipe B be closed after x minutes.
30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16
=> x = 14/16 * 24 = 21.
Answer: E
Answer: E
Question: A certain sum becomes four times itself at simple interest in eight years. In how many years does it become ten times itself?
Options:
A)24
B)55
C)77
D)99
E)01
Rationale: Let the sum be Rs. x, then it becomes Rs. 4x in eight years Rs. 3x is the interest on x for eight years.
R = (100 * 3x)/(x * 8) = 300/8 %
If the sum becomes ten times itself, then interest is 9x.
The required time period = (100 * 9x)/(x * 300/8) = (100 * 9x * 8)/(x * 300) = 24 years.Answer: A
Answer: A
Question: The sume of the ages of 5 children born at the intervals of 3 years each is 50 years.What is the age of the youngest child ?
Options:
A)4 years
B)8 years
C)10 years
D)None of these
E)11 years
Rationale: Solution
Let the ages of the children be x,(x + 3),(x + 6)(x + 9) and (x + 12) years.
Then,x + (x + 3)+(x + 6)+(x + 9)+(x + 12) =50 ⇔ 5x = 20 ⇔ x =4.
∴ Age of the youngest child =x=4 years. Answer A
Answer: A
Question: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 400 feet. What is its area, in square feet?
Options:
A)76,800
B)19,600
C)20,000
D)20,400
E)20,800
Rationale: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.
diagonal = 200
2x + 2y = 560, or x + y = 280
a^2 + b^2 = c^2 for each the sides of the triangle
using the ratio 3:4:5 for sides, and knowing c = 400, you can deduce the following
a=240
b=320
240x320=76,800
A is the answer.
Answer: A
Question: A man cycles at a rate of 4 kmph. He cycles for 45 minutes and then takes a 15 minute break. Determine the total time taken to cover 12 kms by him.
Options:
A)4 hours 35 minutes
B)4 hours
C)3 hours
D)3 hours 45 minutes
E)4 hours 45 minutes
Rationale: Explanation:
Speed of man = 4kmph
Time for which he cycled = 45 minutes.
Distance covered = speed*time
=> 4*45/60
=> 3km
Total time to cover 3 km = 45 minutes + 15 minutes = 60 minutes = 1 hour
Thus 3 km is covered in 1 hour
Required distance to be covered = 12 km
Beginning from origin point, he covers 9 km in 3 hours taking 15 minutes rest after every 45 minutes. To complete 12 kms he goes another 3 km in 45 minutes.
Thus, total time he takes is 3 hours 45 minutes.
ANSWER D
Answer: D
Question: An article is sold at certain price. By selling it at 2/3 of its price one losses 10%, find the gain at original price?
Options:
A)35
B)25
C)10
D)20
E)30
Rationale: let the original Selling Price be $x. then now Selling Price = $2x/3, loss=10%
now C.P=$20x/27*27/20x*100)%=35%
Answer A) 35.
Answer: A
Question: Eight machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 16 days?
Options:
A)4
B)6
C)8
D)10
E)2
Rationale: Rate of one machine = 1 job / (20*8) days
let X = number of machines needed to complete the job in 16 days
1/(8*20) * 16 * X = 1 job
X = 10
10-8= 2
ANSWER: E
Answer: E
Question: A local bank that has 11 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 11 codes?
Options:
A)3
B)11 ( 2 integers 4 codes)
C)5
D)6
E)7
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Total = 16 Codes. Enough. Answer: B
4 integers create 11 codes.
Answer: B
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $400, by what percent is the price to be reduced?
Options:
A)10%
B)15%
C)20%
D)25%
E)80%
Rationale: price of a coat in a certain store = $500
the price of the coat is to be reduced by $400
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (400)*100 / 500 = 80%
Answer: Option E
Answer: E
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 4% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
Options:
A)22.04%
B)26.12%
C)28%
D)16.25%
E)30%
Rationale: Per quarter, interest = 4% So for a year, interest = 16% Due to quarter cumulation, effective yield (YTM) would be slight higher than 16.25% Answer = 16.25% =ANSWER:D
Answer: D
Question: If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is?
Options:
A)20%
B)80%
C)90%
D)22%
E)24%
Rationale: Let C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%.Answer: A
Answer: A
Question: The marks obtained by Vijay and Amith are in the ratio 8:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
Options:
A)12:5
B)12:1
C)6:5
D)12:2
E)6:3
Rationale: 8:5
3:2
-------
24:15:10
24:10
12:5
Answer: A
Answer: A
Question: Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 60 percent carbonated water, what percent of the volume of the mixture is P?
Options:
A)20%
B)30%
C)40%
D)50%
E)60%
Rationale: 60% is 20%-points below 80% and 5%-points above 55%.
So the ratio of solution P to solution Q is 1:4.
Mixture P is 1/5 = 20% of the volume of mixture PQ.
The answer is A.
Answer: A
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
Options:
A)2 PM
B)1 PM
C)7 PM
D)5 PM
E)8 PM
Rationale: 1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM
Answer:D
Answer: D
Question: The average age of twenty four boys in a class and the teacher is 15. If the teacher age is excluded, the average reduces to 14. What is the techer's age?
Options:
A)41
B)36
C)32
D)39
E)38
Rationale: 25*15-24*14= 39
ANSWER:D
Answer: D
Question: Three candidates contested in an election and received 4136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
Options:
A)45%
B)49%
C)50%
D)51%
E)62%
Rationale: Total number of votes polled = 4136+7636+11628 = 23400
Required percentage = 11628*100/23400 = 50%
Answer is C
Answer: C
Question: A student has 7 trousers and 11 shirts. In how many different ways can the student select a trouser and a shirt?
Options:
A)68
B)77
C)86
D)95
E)104
Rationale: The student can select one trouser in 7 ways.
The student can select one shirt in 11 ways.
The number of ways to select one trouser and one shirt is 7 * 11 = 77 ways
The answer is B.
Answer: B
Question: If it is a 3x3 matrix, for which elements in first row are (V, 50, W), second row (196,X, Y)and in third row are (269, Z, 123).It is given that the sum of the numbers in each row, column, diagonal are same. Then find the value of (Y + Z).
Options:
A)1012
B)1011
C)1212
D)1122
E)1021
Rationale: v 50 w
196 x y
269 z 123
in 1st row and 1st column
v+196+269=v+50+w
w=415
Again, in 2nd column and 3rd row
50+x+z=269+z+123
x=342
As sum of each row column and diagonal are same.
So, 269+342+415=1026
415+y+123=1026
y=488
269+z+123=1026
z=634
y+z=488+634=1122
ANSWER:D
Answer: D
Question: Ross has 320 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.
Options:
A)48 ; 80.
B)49 ; 80.
C)50 ; 80.
D)51 ; 80.
E)52 ; 80.
Rationale: Total shirts = 320
Green shirts = 3/4*320 = 240, Non green shirts = 80
Shirts without button = 1/10*320 = 32, shirts with button = 288
Required: Range of shirts with buttons that are not green.
Maximum non green shirts with buttons = number of non green shirts = 80
Minimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 80 - 32 = 48
Hence the range would be (48, 80)
Correct Option: A
Answer: A
Question: If 1^3 + 2^3 + 3^3 +......+ 10^3 = 516 then the value of 2^3 + 4^3 + 6^3 + ..... + 20^3 is
Options:
A)1032
B)1040
C)1048
D)1050
E)1052
Rationale: 2(13 + 23 + 33 + ---------- + 103)
2 × 516 = 1032
A
Answer: A
Question: If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
6 – 9 + 8 × 3 ÷ 20 =
Options:
A)6
B)10
C)12
D)-2
E)8
Rationale: B 10
Answer: B
Question: Two pillars are standing side-by-side. One pillar, which is 6 feets tall, casts a shadow that is 12 feets long. The other pillar is 4 feets tall. Compute, in feets, the length of the shadow that
the shorter pillar casts.
Options:
A)8
B)10
C)12
D)16
E)20
Rationale: The ratio of shadow to height is constant, so if x is the length of the shadow, then
6/12 = 4/x and x = 8 .
correct answer A
Answer: A
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
A)43
B)30
C)35
D)45
E)50
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.
ANSWER A
Answer: A
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
Options:
A)3/8
B)3/4
C)3/5
D)3/9
E)3/1
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Answer: B