divelab/Sys2Bench huggingface dataset:
Question: If (x + 10)^2 = 144, which of the following could be the value of 2x?
Options:
A)–26
B)–22
C)–44
D)66
E)13
Rationale: You can also get to the answer by backsolving using answer choices
Starting with x= -22
(x + 10)^2 = 144
(-22 + 10)^2 = 144 =====> (-12)^2 = 144 Bingo, Clearly, among the answer choices only -22 will result in 144 in the equation so x must be -22,
Then 2x = 2 * -22 = -44
Answer: C
Answer: C
Question: Let f(x,y) be defined as the remainder when (x–y)! is divided by x. If x=36, what is the maximum value of y for which f(x,y)=0?
Options:
A)9
B)12
C)18
D)20
E)30
Rationale: The question is finding y such that (36-y)! is a multiple of 36. That means we need to have 2^2*3^2 in (36-y)!
6! is the smallest factorial number with 2^2*3^2 as a factor.
36-y = 6
y = 30
The answer is E.
Answer: E
Question: What percent is 6 gm of 1 kg?
Options:
A)0.06%
B)0.6%
C)0.006%
D)6%
E)None of these
Rationale: Explanation:
1 kg = 1000 gm
6/1000 * 100 = 600/1000
=3/5 = 0.6 %
Answer: Option B
Answer: B
Question: Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
Options:
A)30
B)35
C)37
D)41
E)42
Rationale: Explanation:
Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ lO) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years
Option B
Answer: B
Question: The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 5 is:
Options:
A)545
B)488
C)542
D)548
E)560
Rationale: Required number = (L.C.M. of 12, 15, 20, 54) + 5
= 540 + 5
= 545.
answer :A
Answer: A
Question: A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.
Options:
A)12 1/2 days
B)12 1/9 days
C)12 8/2 days
D)17 1/2 days
E)32 1/2 days
Rationale: 15/25 + 10/x = 1 => x = 25
1/25 + 1/25 = 2/25
25/2 = 12 1/2 days
Answer: A
Answer: A
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?
Options:
A)2:6
B)2:3
C)2:5
D)2:1
E)2:4
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3.
Answer:B
Answer: B
Question: If 7875 / 5.25 = 1500, then 787.5 / 52.5 is equal to ?
Options:
A)15
B)19
C)12
D)14
E)16
Rationale: Answer
Given expression 787.5 / 52.5 = 7875 / 525
= 7875 / (525 x 100)
= 1500 / 100
15
Correct Option: A
Answer: A
Question: The ratio of number of boys and girls in a school is 2:5. If there are 490 students in the school, find the number of girls in the school?
Options:
A)150
B)350
C)300
D)370
E)280
Rationale: Let the number of boys and girls be 2x and 5x
Total students = 490
Number of girls in the school = 5*490/7 = 350
Answer is B
Answer: B
Question: What percent is 320 gm of 1 kg?
Options:
A)25%
B)40%
C)10%
D)8%
E)32%
Rationale: 1 kg = 1000 gm
320/1000 Ã— 100 = 32000/1000
=32 %
Answer is E
Answer: E
Question: A train moves 100m in 2 sec and then find the speed travelled?
Options:
A)28
B)900
C)50
D)180
E)none
Rationale: Length = Speed * time
Speed = L/T
S = 100m/2sec
S = 50 M/Sec
Speed= 50*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 180Kmph.Answer:D
Answer: D
Question: A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done?
Options:
A)572
B)672
C)472
D)372
E)None
Rationale: Solution:
10C5: when both are not included.
10C4: when one of them is included.
Number of ways = 10C5 +10C4+ 10C4 = 672
Answer: Option B
Answer: B
Question: 7 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
Options:
A)1:2
B)1:3
C)2:1
D)2:3
E)None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 7x + 2y = 4(x+y)
=> 3x = 2y
=> x/y = 2/3
=> x:y = 2:3
Option D
Answer: D
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
A)33/16
B)33/91
C)33/29
D)33/18
E)33/11
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= ¹²C₄/¹⁵C₄
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer: B
Answer: B
Question: An empty pool being filled with water at a constant rate takes 8hours to fill to 4/5 of its capacity.how much more time will it take to finish filling the pool?
Options:
A)5hr 30min
B)5hr 20min
C)4hr 48min
D)3 hr 12min
E)5hr 40 min
Rationale: As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill.
To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).
Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 5 hours 40 minutes.
Answer: E.
Answer: E
Question: The radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their heights.
Options:
A)1:4
B)1:3
C)1:2
D)1:5
E)None of these
Rationale: Explanation:
Let their radii be 2x, x and their heights be h and H resp.
Then,
Volume of cone =1/3πr2h
1/3∗π∗(2x)2∗h /1/3∗π∗x2∗H
=>hH=14
=>h:H=1:4
Option A
Answer: A
Question: A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs. 2.40 the number of girls is
Options:
A)35
B)40
C)45
D)50
E)55
Rationale: Explanation:
Step (i): Let x be the number of boys and y be the number of girls.
Given total number of boys and girls = 100
x+y=100 -------------- (i)
Step (ii): A boy gets Rs. 3.60 and a girl gets Rs. 2.40
The amount given to 100 boys and girls = Rs. 312
3.60x + 2.40y = 312 -------------- (ii)
Step (iii):
Solving (i) and (ii)
3.60x + 3.60y = 360 --------- Multiply (i) by 3.60
3.60x + 2.40y = 312 --------- (ii)
1.20y = 48
y = 48 / 1.20
= 40
Number of girls = 40
Answer: B
Answer: B
Question: A and B together can do a piece of work in 6 days and A alone can do it in 13 days. In how many days can B alone can do it?
Options:
A)12 days
B)15 days
C)78/7 days
D)21 days
E)22/7 days
Rationale: Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/13 work in 1 day
B alone can do (1/6 -1/13) =7/78 work in 1 day
=> complete work can be done in 78/7 days by B
Answer: Option C
Answer: C
Question: From a Group of 8 People, Including Gary and Nina, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include Gary but not Nina
Options:
A)5/56
B)9/56
C)15/56
D)21/56
E)25/56
Rationale: Number of ways of selecting 3 people out of 8 people = 8C3
In the three members Gary will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Nina cannot be there in the team. So 2 members have to be selected and the number of available members = 7 - Nina = 6
Number of ways to form a 3 member team that includes Gary and excludes Nina = 6C2
Probability = 6C2/8C3 = 15/56
Answer: C
Answer: C
Question: A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?
Options:
A)28
B)32
C)48
D)60
E)120
Rationale: Sisters can sit separately in two ways:
1. one of them is on the front seat (2 ways). Others (including second sister) can be arranged in: 2 (drivers seat)*3! (arrangements of three on the back seat)=12 ways. Total for this case: 2*12=24
Or
2. both by the window on the back seat (2 ways). Others can be arranged in: 2 (drivers seat)*2 (front seat)*1(one left to sit between the sisters on the back seat)=4 ways. Total for this case: 2*4=8.
Total=24+8=32. ANS:B
Answer: B
Question: How many bricks each measuring 20cm x 10cm x 8cm, will be needed to build a wall 10m x 8m x 24.5m
Options:
A)12250
B)13400
C)12500
D)14340
E)None of these
Rationale: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (1000 x 800 x 24.5) / (20 x 10 x 8) = 12250
Answer: A
Answer: A
Question: In Richard's office one half of the workers are Indians,quarter are from America,one-fifth are from Canada and the other 100 are China. How many workers total are there in the company?
Options:
A)250
B)500
C)750
D)1000
E)2000
Rationale: 1/2x + 1/4x +1/5x = 19/20x
Remaining 1/20 x= 100
x= 100*20= 2000
E is the answer.
Answer: E
Question: Rahim bought 32 books for Rs.1500 from one shop and 60 books for Rs.340 from another. What is the average price he paid per book ?
Options:
A)s.17
B)s.18
C)s.12
D)s.11
E)s.20
Rationale: Average price per book
= (1500+ 340) / (32 + 60) = 1840/ 92
= Rs.20
Answer:E
Answer: E
Question: Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 30 minutes earlier than usual. How much time did the man spend walking?
Options:
A)45 minutes
B)50 minutes
C)40 minutes
D)55 minutes
E)35 minutes
Rationale: As they arrived 30 minutes earlier than usual, they saved 30 minutes on round trip from home to station (home-station-home) --> 15 minutes in each direction (home-station) --> wife meets husband 15 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-15 minutes= 45 minutes.
Answer: A
Answer: A
Question: How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
Options:
A)sec
B)sec
C)sec
D)sec
E)sec
Rationale: The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A
Answer: A
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
Options:
A)5600
B)6000
C)6400
D)7200
E)8600
Rationale: Number of bricks =Volume of the wall/Volume of 1 brick =	(800 x 600 x 22.5)/(25 x 11.25 x 6) = 6400.
Answer: Option C
Answer: C
Question: A can do a work in 14 days. B is 40% more efficient than A. How many days does B alone take to do the same job?
Options:
A)9
B)10
C)11
D)12
E)8
Rationale: Ratio of times taken by A and B = 140:100 = 7:5
suppose B alone to take x days to do the work
then, 7:5::14:x
7x= 5*14
x=10 days
correct option is B
Answer: B
Question: Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 72 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?
Options:
A)24%
B)16%
C)11%
D)7%
E)5%
Rationale: Let I be the number of incandescent bulbs.
Let F be the number of fluorescent bulbs.
0.4I + 0.8F = 0.72(I+F)
0.08F = 0.32I
F = 4I
This means that for every 1 incandescent bulb, there are 4 fluorescent bulbs.
The percent of bulbs that are switched on which are incandescent is:
0.4I / (0.4I + 0.8F) = 0.4I / (0.4I + 0.8*4I) = 0.4I / 3.6I = 1/9 which is about 11%.
The answer is C.
Answer: C
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate?
Options:
A)321
B)430
C)530
D)172
E)480
Rationale: Let the total no of mangoes in the crate be x
Then the no of bruised mango = 1/30 x
Let the no of unsalable mangoes =3/4 (1/30 x)
1/40 x =12
x=480
Option E
Answer: E
Question: If -1 < x < 1, which of the following must be true?
I. x^3 < x^2
II. x^5 < 1 – x
III. x^4 < x^2
Options:
A)I only
B)I and II only
C)II and III only
D)I and III only
E)I, II and III
Rationale: I. x^3 < x^2 --> from -1 < x < 1 x must be a decimal so multiplying it by itself makes it a smaller value positive or negative. x^2 is always positive so x^3 being a small value always makes x^3<x^2 so this statement is true.
II. x^5 < 1 – x --> x(x^4+1) < 1 --> since 1(1+1)=2 > 1, so this statement is false.
III. x^4 < x^2 --> reduce by x^2 (we can safely do that since from -1 < x < 1 is follows that x^2>0): x^2 < 1. Again, as -1 < x < 1, then x^2 must be less than 1. Hence, this statement is also true.
Answer: D.
Answer: D
Question: If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
( example 99 = 9+9 = 18=1+8=9, so #=9)
Options:
A)4/10
B)4/9
C)1/2
D)6/10
E)5/9
Rationale: First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability = 50/90 = 5/9
Correct answer E
Answer: E
Question: Lucy deposited $67600 in an investment fund that provided 16 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $5300?
Options:
A)90.5
B)92
C)93
D)90
E)96.1
Rationale: A = P + I = 67600 + 5300 = 72900
72900 = 67600(1 + 8/4*100)^(4t)
(729/676) = (102/100)^(4t)
t =7 1/2 yrs = 90 months
Answer: D
Answer: D
Question: For any positive x, y and z if x is n% of y and z is m% of y then what percentage Q must x be of z?
Options:
A)(n/m)%
B)(m × n)%
C)(100 / [m × n]) %
D)(100 × m/n)%
E)(100 × n/m)%
Rationale: x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer Q is 100n/m %.E
Answer: E
Question: Simplify: 0.6*0.6+0.6*0.6
Options:
A)0.52
B)0.42
C)0.48
D)0.64
E)0.46
Rationale: Given exp. = 0.6*0.6+(0.6*6) = 0.36+0.1 = 0.46
Answer is E.
Answer: E
Question: The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers?
Options:
A)9
B)10
C)15
D)18
E)20
Rationale: The only possible sum for 4 different squares of an integer with total sum number is 95 are :
49 + 36 + 9 + 1 = 95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 17)
or
81 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15)
hence the answer is (C)
Answer: C
Question: This is an ancient problem dating back to about 310 A.D.
Demochares had lived one-fourth of his life as a boy, one-fifth as a young, one-third as a man. and has spent thirteen years in his dotage. How old is Demochares?
Options:
A)44
B)53
C)75
D)60
E)50
Rationale: D
60
Demochares must be sixty years of age.
Answer: D
Question: A book is bought for Rs.600/- and sold at a profit of 10% find its selling price?
Options:
A)s.740/-
B)s.660/-
C)s.680/-
D)s.720/-
E)s.620/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
110 % ------> 660 (110 * 6 = 660)
Selling price = Rs.660/-
Option 'B'
Answer: B
Question: Rekha took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 588 as interest at the end of the loan period, what was the rate of interest?
Options:
A)5
B)6
C)4
D)3
E)7
Rationale: Let rate = R% and time = R years.
Then, (1200 * R * R) / 100 = 588
12R2 = 588
R2 = 49 => R = 7.
Answer:E
Answer: E
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Options:
A)5.2 hrs
B)2.9 hrs
C)1.9 hrs
D)7.2 hrs
E)1.4 hrs
Rationale: Net part filled in 1 hour = (1/4 - 1/9) = 5/36
The cistern will be filled in 36/5 hrs i.e., 7.2 hrs.
Answer:D
Answer: D
Question: If P(32, 6) = kC (32, 6), then what is the value of k?
Options:
A)6
B)32
C)120
D)720
E)None
Rationale: Since 32P6 = k32C6
⇒ 32/ ( 32-6 ) = k(32/ ( 32-6 )
⇒k = 6! = 720
Answer D
Answer: D
Question: In what time will a train 200 meters long cross an electric pole, if its speed is 128 km/hr
Options:
A)5 seconds
B)5.7 seconds
C)3 seconds
D)2.5 seconds
E)None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 128*(5/18) = 35 m/sec
Time = Distance/speed
= 200/35 = 5.7 seconds
Option B
Answer: B
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
Options:
A)270
B)287
C)269
D)200
E)271
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.
Answer: A
Answer: A
Question: The area of a parallelogram is 243sq m and its altitude is three times the corresponding base. What is the length of the base?
Options:
A)4
B)9
C)10
D)4
E)12
Rationale: 3x * x = 243 => x
= 9
Answer: B
Answer: B
Question: There are 8 disks in a container that are numbered 23, 24, 25, 26, 28, 29, 30 and 31. 4 disks are randomly removed from the container, one after the other, without replacement. Then a list of 5 numbers containing the 4 numbers on the disks selected, together with the number 27 will be made. What is the probability that 27 is the median of the list of 5 numbers?
Options:
A)2/5
B)17/35
C)1/2
D)18/35
E)5/9
Rationale: we must consider that there are two ways to choose from A or B, and then two ways to choose each number from their respective groups:
Group A (23,24,25,26) and Group B (28,39,30,31). Then we saw that in order to have a median of 27 we need to have 2 from group and and 2 from group B.
The probability of that is 4/8 x 3/7 x 4/6 x 3/5 x (1/2) x (1/2) = 18/35.
Answer: D.
Answer: D
Question: Which of the following is closest to 1/6+1/66+1/666
Options:
A)1/4.5
B)1/7
C)1/5.67
D)1/9
E)1/8
Rationale: 1/6+1/66+1/666=0.16+0.015+0.0015=0.1765=1/5.665
Answer C
Answer: C
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 35 more. What was his original selling price?
Options:
A) $770
B) $550
C) $700
D) $1100
E) $840
Rationale: Let the original purchase price be X
So original selling price at 10% profit = 1.1X
If product is purchased at 10% less of original = 0.9X
Profit of 30% on this price = 1.3(0.9X)
He would have received $35 more in second scenario => 1.3(0.9X) - 1.1X = 35
=> 0.07X = 35
=> X = $500
Original purchase price = $500
Hence, original selling price (at 10% of profit) = 1.1(500) = $550
Option B
Answer: B
Question: Craig sells major appliances. For each appliance he sells, Craig receives a commission of $50 plus 10 percent of the selling price. During one particular week Craig sold 6 appliances for selling prices totaling $3,620. What was the total of Craig's commissions for that week?
Options:
A)$412
B)$526
C)$585
D)$605
E)$662
Rationale: Craig receives a commission of $50 on each appliance plus a 10% commission on total sales, thus his commission was 6*50 + 0.1*3,620 = 662.
Answer: E.
Answer: E
Question: If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is?
Options:
A)127
B)688
C)200
D)121
E)123
Rationale: Let C.P. be Rs. x.
Then, 5% of x = 350 - 340 = 10
x/20 = 10 => x = 200
Answer: C
Answer: C
Question: The side of a square is increased by 15% then how much % does its area increases?
Options:
A)30.75 %
B)35.85 %
C)37.55 %
D)35.65 %
E)32.25 %
Rationale: a = 100 a2 = 10000
a = 115 a2 = 13225
----------------
10000 --------- 3225
100 -------? => 32.25 %
Answer:E
Answer: E
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)8 days
B)10 days
C)20/3 days
D)14 days
E)16 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 Ã— 20/30 = 20/3 days
C)
Answer: C
Question: Three cannons are firing at a target. If their individual probabilities to hit the target are 0.4, 0.2, and 0.3 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94
Options:
A)0.06
B)0.336
C)0.21
D)0.29
E)0.94
Rationale: The probability that eachdoesn'thit is: 0.4, 0.2, and 0.3. When we have multiple independent events, we multiply the probabilities:
.6*.8*.7 = 0.336.
Option: B
Answer: B
Question: The average weight of three boys P, Q and R is 54 kg, while the average weight of three boys Q, S and T is 60 kg. What is the average weight of P, Q, R, S and T?
Options:
A)338
B)279
C)279
D)342
E)211
Rationale: Explanation:
Total weight of (P + Q + R) = {54*3} kg = 162 kg
Total weight of(Q + S + T) = (60 *3) kg = 180 kg
Adding both, we get : P + 2Q + S + R + T = (162 + 180) kg = 342 kg
So, to find the average weight of P, Q, R, S & T, we ought to know Q's weight, which is not given.
The data is inadequate.
ANSWER:D
Answer: D
Question: The length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)50 m
B)60 m
C)65 m
D)75 m
E)80 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: B