mathewhe/aqua_rat huggingface dataset:
Question: What is the probability that you will get a sum of 8 when you throw three dice simultaneously?
(A) 21/6^3.
(B) 23/6^3.
(C) 25/6^3.
(D) 27/6^3.
(E) 29/6^3.
Rationale: This sum of 8 can occur in the following cases:
1-1-6 --> 3!/2!=3 ways;
1-2-5 --> 3!=6 ways;
1-3-4 --> 3!=6 ways;
2-2-4 --> 3!/2!=3 ways;
2-3-3 --> 3!/2!=3 ways.
Total of 3+6+6+3+3=21 ways.
Now, since the total number of outcomes is 6^3, then the probability is 21/6^3.
ANSWER:A
Answer: (A) 21/6^3.
Question: In a certain code language, “ORANGE” is written as “NTETOO”. How would “BLACK” be written in that language ?
(A) ANEIS
(B) UGDII
(C) GIKHK
(D) HOUH
(E) AHKSS
Rationale: Explanation:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
letter position
ANSWER: A
Answer: (A) ANEIS
Question: If 50% of x equals the sum of y and 20, then what is the value of x–2y?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 90
Rationale: Explanation :
Given, 50% of x equals the sum of y and 20.
=>(50/100)×x=y+20.
=>x/2=y+20.
=>x=2y+40.
=>x–2y= 40.
Answer : B
Answer: (B) 40
Question: The speed at which a man can row a boat in still water is 6.5 kmph. If he rows downstream, where the speed of current is 2.5 kmph, what time will he take to cover 90 metres?
(A) 90 seconds
(B) 36seconds
(C) 26 seconds
(D) 18 seconds
(E) 6.5 seconds
Rationale: Speed of the boat downstream = 6.5 + 2.5
= 9 kmph
= 9 * 5/18 = 2.5 m/s
Hence time taken to cover 90m =90/2.5
= 36 seconds.
Answer:B
Answer: (B) 36seconds
Question: If -4 < x < 7 and -5 < y < 3, which of the following specifies all the possible values of xy?
(A) -42 < xy < 21
(B) -42 < xy < 24
(C) -28 < xy < 18
(D) -24 < xy < 21
(E) -35 < xy < 20
Rationale: The least value of xy is a bit more than 7*(-5)=-35 and the largest value of xy is a bit less than (-4)*(-5)=20.
Therefore -35 < xy < 20.
Answer: E.
Answer: (E) -35 < xy < 20
Question: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is
(A) 12
(B) 28
(C) 42
(D) 72
(E) 11
Rationale: required area = 14*14 - (4 * 1/4 * 22/7 * 7 *7) sq cm
= 196 - 154
= 42 sq cm.
Answer: C
Answer: (C) 42
Question: When 28 is divided by the positive integer s, the remainder is 1. What is the sum of all the possible values of s for which this is true?
(A) 2
(B) 3
(C) 9
(D) 30
(E) 39
Rationale: The only possible values of the form 28=sp+1 are 3,9 or 27
The sum = 3+9+27 =39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.
Answer: (E) 39
Question: A man takes 3 hours 45 minutes to row a boat 10 km downstream of a river and 2 hours 30 minutes to cover a distance of 3 km upstream. Find the speed of the current.
(A) 1 km/hr
(B) 1/2 km/hr
(C) 3/4 km/hr
(D) 4 km/hr
(E) None of these
Rationale: Explanation:
First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]
So we need to calculate speed downstream and speed upstream first.
Speed = Distance / Time [important]
Speed upstream =(10/3 3/4)km/hr
=8/3km/hr
Speed Downstream = (3/2 1/2)km/hr
=6/5km/hr
So speed of current = 1/2(8/3−6/5)
=3/4km/hr
Option C
Answer: (C) 3/4 km/hr
Question: if At what time between 7 & 2 will the hands of a watch point in opposite directions?
(A) 50 4/11 min past 4
(B) 50 4/11 min past 1
(C) 50 4/81 min past 7
(D) 50 4/81 min past 2
(E) 50 4/11 min past 6
Rationale: At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30min. spaces apart.
Minute hand will have to gain 5 min. spaces.
55min spaces are gained in 60 min.
5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min.
Required time = 54 6/11 min. past 4.
Answer: Option 'A'
Answer: (A) 50 4/11 min past 4
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 33
(B) 878
(C) 30
(D) 88
(E) 11
Rationale: C = 1/5 – 1/6 = 1/30 => 30 days
Answer: C
Answer: (C) 30
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 12 m
(B) 25 m
(C) 127.5 m
(D) 32m
(E) 56m
Rationale: Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.
ANSWER C
Answer: (C) 127.5 m
Question: An urn contains 5 black and 3 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
(A) 1/5
(B) 3/7
(C) 5/14
(D) 3/5
(E) 2/7
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 5/8
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 4 black balls and Eight white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 4/7
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 5/8 × 4/7 = 5/14
C
Answer: (C) 5/14
Question: Set S consists of integers {4, 7, 10, 14, 15}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 50%. What is the value of integer n?
(A) 28
(B) 32
(C) 36
(D) 40
(E) 44
Rationale: The average of the numbers in set S is 10.
If we increase the mean by 50%, the new mean is 15.
Thus, on average, 5 numbers increase by 5.
Therefore n = 15+25 = 40
The answer is D.
Answer: (D) 40
Question: What is least possible value of |23 - 7y| is
(A) 0
(B) 1
(C) 2
(D) 5
(E) 9
Rationale: Since y can be ANY number, we can minimize the value of |23 - 7y| by setting 23 - y equal to zero
If 23 - 7y = 0, then 23 = 7y, which means y = 23/7
In other words, when y = 23/7, we find that |23 - 7y| = 0
Answer:A
Answer: (A) 0
Question: find the terms which do not contain 7 between 1000 and 9999
(A) 9000
(B) 8000
(C) 8500
(D) 8800
(E) 8900
Rationale: Total number of four digit numbers =9000 (i.e 1000 to 9999 )
We try to find the number of numbers not having digit 2 in them.
Now consider the units place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Tens place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Hundreds place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Thousands place can be selected in 8 ways (i.e 1,2,3,4,5,6,,8,9) here '0' cannot be taken
Total number of numbers not having digit 7 in it =9 x 9 x 9 x 8 =5832
Also,Total number of numbers having digit 7 in it = 9000-5832 =3168
ANSWER:A
Answer: (A) 9000
Question: If the sum of six numbers is between 135 and 164, then the average (arithmetic mean) of the six numbers could be which of the following?
(A) 15.4.
(B) 20.5.
(C) 25.5.
(D) 31.25.
(E) 32.5.
Rationale: 135/6=22.5
164/6=27.33
Only C fits in between these two limits.
Answer: C
Answer: (C) 25.5.
Question: When is |y-8| = 8-y?
(A) y=0
(B) y<0
(C) y>8
(D) y<8
(E) y<=8
Rationale: When is |x-8| = 8-x?
Choice A: X=8, it is true but X cannot be always 8
Choice B: X=0, it is also true, but X cannot be always 0
Choice C: X>8, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2
Choice D: X<=8, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is E.
Answer: (E) y<=8
Question: Sum of the squares of three numbers is 522 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 22
(C) 25
(D) 27
(E) 28
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 522 + 2* 131
a + b + c = √784 = 28
E
Answer: (E) 28
Question: What number fits best in the missing place?
_	4	5	3	5
9	5	7	10	3
(A) 3
(B) 8
(C) 4
(D) 5
(E) 6
Rationale: C
4
5 = Five (four letters) => 4
7 = Seven (five letters) => 5
10 = Ten (three letters) => 3
3 = Three (five letters) => 5
Therefore, 9 = Nine (four letters) => 4.
Therefore the missing number is 4.
Answer: (C) 4
Question: A man rows his boat 84 km downstream and 48 km upstream, taking 2 hours each time. Find the speed of the stream?
(A) 6 kmph
(B) 5 kmph
(C) 9 kmph
(D) 8 kmph
(E) 1 kmph
Rationale: Speed downstream = d/t = 84/(2) = 42 kmph
Speed upstream = d/t = 48/(2) = 24 kmph
The speed of the stream = (42 - 24)/2 = 9 kmph
Answer:C
Answer: (C) 9 kmph
Question: How many of the positive factors of 25 , 150 and how many common factors are there in numbers?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 1
Rationale: factors of 25 - 1, 5, 25
factors of 150 - 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Comparing both, we have three common factors of 25 and 150- 1,5,25
Answer(C)
Answer: (C) 3
Question: When n is divided by 12, the remainder is 2. What is the remainder when 4n is divided by 5?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let n=2 (leaves a remainder of 2 when divided by 15)
4n = 4(2) =8, which leaves a remainder of 3 when divided by 5.
Answer C
Answer: (C) 3
Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is?
(A) 4pm
(B) 3pm
(C) 5pm
(D) 6pm
(E) 7pm
Rationale: Time from 7 am to 4.15 pm = 9 hrs 15 min = hrs
3 min. 5 sec. of this clock = 3 min. of the correct clock.
Now 3min.5sec. is hrs of this clock = 3 min.is hrs of the correct clock
hrs of clock = hrs of the correct clock.
= 9 hrs of the correct clock.
The correct time is 9 hrs after 7 am. i.e., 4 pm.
Answer: A
Answer: (A) 4pm
Question: The measure of the side of a square is quadrupled. If x represents the perimeter of the original square, what is the value of the new perimeter?
(A) 3x
(B) 4x
(C) 9x
(D) 12x
(E) 27x
Rationale: Original perimeter = x
Hence original side = x/4
New side = 4x/4
New perimeter = 4*4x/4 = 4x
Correct Option: B
Answer: (B) 4x
Question: A train travels from Albany to Syracuse, a distance of 100 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?
(A) 31.25
(B) 30
(C) 32
(D) 34
(E) 36
Rationale: 50*T =100 THEREFORE T = 100/50 =2
ON RETURN SPEED * ( 5.4 -2) =100 THEREFORE T = 100/3.2 =31.25
A
Answer: (A) 31.25
Question: What is the present worth of Rs. 396 due in 2 years at 5% simple interest per annum?
(A) 128
(B) 277
(C) 120
(D) 360
(E) 371
Rationale: Let the present worth be Rs. x. Then,
S.I. = (396 - x)
(x * 5 * 2) / 100 = (396 - x)
10x = 39600 - 100x
110x = 39600 => x = 360.
Answer: D
Answer: (D) 360
Question: If x is less than y by 45% then y exceed x by:
(A) 33.33%
(B) 25%
(C) 81.81%
(D) 66.66%
(E) None of these
Rationale: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)
=> 45/(100-45)*100
=81.81%
ANSWER:C
Answer: (C) 81.81%
Question: Meg and Bob are among the 4 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
(A) 12
(B) 30
(C) 60
(D) 90
(E) 120
Rationale: Total # of ways the race can be finished is 4!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 4!/2=12.
Answer: A.
Answer: (A) 12
Question: If GAVE is coded as 4657 and BAT is coded as 229. How is GATE coded?
(A) 4697
(B) 4967
(C) 4976
(D) 7496
(E) 4796
Rationale: g-4 a-6 e-7 from the code gate
t - 9 from bat
ANSWER:A
Answer: (A) 4697
Question: Last year the price per share of Stock N increased by x percent and the earnings per share of Stock N increased by y percent, where x is greater than y. By what percent did the ratio of price per share to earnings per share increase, in terms of x and y?
(A) x/y%
(B) (100+y) %
(C) 100*(x-y)%
(D) 100*(x-y)/(100+y) %
(E) (x-y)/(100+y) %
Rationale: Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases
After the increase the new price is: P*(1+x/100) and the new earning is: E*(1 +y/100)
The new P/E is: (1+x/100)P/(1+y/100)E
The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:
[(1+x/100)/(1+y/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:
100*(x-y)/(100+y) %
Answer : D
Answer: (D) 100*(x-y)/(100+y) %
Question: What is the sum of all three digit integers formed using the digits 1, 2, and 3 (repetition is allowed)
(A) 4443
(B) 5980
(C) 5992
(D) 5990
(E) 5994
Rationale: n = 3*3*3 = 27
<x> = (333 + 111) / 2 = 222
Sum = number of integers x average value
n * <x> = 27 * 222 = 5994
answer = E
Answer: (E) 5994
Question: A trader mixes 26 kg of rice at Rs. 10 per kg with 30 kg of rice of other variety at Rs. 20 per kg and sells the mixture at Rs. 20 per kg. His profit percent is:
(A) No profit, no loss
(B) 30.23%
(C) 8%
(D) 10%
(E) None of these
Rationale: C.P. of 56 kg rice = Rs. (26 x10 + 30 x20) = Rs. (260 + 600) = Rs. 860
S.P. of 56 kg rice = Rs. (56 x 20) = Rs. 1120
Gain =260/860x100% = 30.23%
Answer: Option B
Answer: (B) 30.23%
Question: Aram’s car was fined when he gave Joe and Peter a ride, so they decided to help Aram pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Aram pay?
(A) $13
(B) $15
(C) $20
(D) $28
(E) $48
Rationale: As given Aram' payment is [1][/2]*Fine -4
i.e Total Fine = 2 * (Sam's payment + 4)
Now, as everything looks integer, Fine should be able to divide by 4 and 3 . Because Joe's contribution has 1/4 of the fine and Peter's contribution has 1/3 of the fine
So, that leads me to following :
Options , Aram's pay , Total Fine (F) , F/4 , F/3
A) , 13 , 34 , No i.e 34/4 , No i.e 34/3
B) , 14 , 38 , No , No
C) , 20 , 48 , Yes Yes
,
No need to further go on as we have got F/4 and F/3 correct, just for confirmation we go further
D) , 28 , 64 , Yes , No
E) , 48 , 104 , Yes , No
Correct answer is C
Answer: (C) $20
Question: The number of sailors on a ship is 82% more than the number of officers. The ratio of sailors to officers would be
(A) 33:25
(B) 47:20
(C) 47:25
(D) 22:25
(E) 91:50
Rationale: Sailor = 1.82 * Officer
Sailor/Officer = 1.82/1 = 182/100 = 91/50
Answer will be E
Answer: (E) 91:50
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 40 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 10 sec
(B) 16 sec
(C) 13 sec
(D) 67 sec
(E) 8 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 40
D = 40 * 100/18 = 2000/9
RS = 60 + 40 = 100 * 5/18
T = 2000/9 * 18/500 = 8 sec
Answer: E
Answer: (E) 8 sec
Question: When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 6, the quotient is 3y and the remainder is 5. What is the value of 7y – x ?
(A) 2
(B) 1
(C) 0
(D) -1
(E) -2
Rationale: (1) x = 11y + 4
(2) 2x = 18y + 5
Let's subtract equation (1) from equation (2).
7y + 1 = x
7y - x = -1
The answer is D.
Answer: (D) -1
Question: A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent?
(A) 27%
(B) 20%
(C) 80%
(D) 30%
(E) 25%
Rationale: 900 ---- 225
100 ---- ? => 25%
Answer: E
Answer: (E) 25%
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 6 years at 10% per annum is Rs.80 of money?
(A) 1000
(B) 1200
(C) 4800
(D) 3600
(E) 8400
Rationale: P = 80(100/10)6 => P = 1500
Answer: C
Answer: (C) 4800
Question: A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?
(A) 4.3
(B) 7.2
(C) 2.3
(D) 3.2
(E) 1.1
Rationale: Explanation:
Speed = {\color{Blue} \left ( \frac{600}{5\times 60} \right )m/ sec =2m/ sec=\left ( 2\times \frac{18}{5} \right )km/hr=7.2km/hr}
Answer: B
Answer: (B) 7.2
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 150 m
(B) 350 m
(C) 300 m
(D) 240 m
(E) none
Rationale: Speed =(54 x5/18m/sec) = 15 m/sec.
Length of the train = (15 x 20)m =300 m.
Let the length of the platform be x metres.
Then,x + 300/36= 15
x + 300 = 540
x = 240 m
Answer: D
Answer: (D) 240 m
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 6 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 26 km/hr
(B) 17 km/hr
(C) 90 km/hr
(D) 77 km/hr
(E) 46 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/6 = 3x => x = 25/2.
So, speed of the faster train = 50/2 = 50/2 * 18/5
= 90 km/hr.
Answer:C
Answer: (C) 90 km/hr
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs.441 is required to paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
(A) 12
(B) 18
(C) 20
(D) 21
(E) 24
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 441/3 = 147 sq m
l b = 147i.e., l * l/3 = 147
l^2 = 441 => l = 21.
D
Answer: (D) 21
Question: Find the odd man out. 1, 8, 27, 64, 125, 196, 216, 343
(A) 64
(B) 196
(C) 216
(D) 1
(E) 146
Rationale: Explanation :
The pattern is 1^3, 2^3, 3^3, 4^3, 5^3, 6^3, 7^3.
196 is not a perfect cube
Answer : Option B
Answer: (B) 196
Question: The average age of a committee of 8 members is 40 years. A member aged 55 years retired and his place was taken by another member aged 39 years . The average age of
present committee is;
(A) 39 years
(B) 38 years
(C) 36 years
(D) 35 years
(E) 37 years
Rationale: Total age of the committee = 40*8 = 320,
Total age when a member is retired
and a new one was joined = 320-55 +39, =304
Average age of present committee = 304/8 = 38.
ANSWER:B
Answer: (B) 38 years
Question: What is the unit digit in the product (3^65 x 6^59 x 7^71)?
(A) 18
(B) 12
(C) 69
(D) 32
(E) 4
Rationale: Explanation:
Unit digit in 3^4 = 1 Unit digit in (3^4)16 = 1
Unit digit in 3^65 = Unit digit in [ (3^4)16 x 3 ] = (1 x 3) = 3
Unit digit in 6^59 = 6
Unit digit in 7^4 Unit digit in (7^4)17 is 1.
Unit digit in 7^71 = Unit digit in [(7^4)17 x 73] = (1 x 3) = 3
Required digit = Unit digit in (3 x 6 x 3) = 4
E
Answer: (E) 4
Question: __2A
x__B
____
CC
In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 3, what is the value of C?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: If A+B=3
assuming A and B are positive then A*B<10 (they could be either 1,2,)
therefore
A*B=C
2*B=C
A+B=3
Three simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=1 --> C=2 (ANSWER E)
Answer: (E) 2
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
(A) 4082.42
(B) 4082.38
(C) 4082.78
(D) 4082.4
(E) 4082.94
Rationale: Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
Answer: Option D
Answer: (D) 4082.4
Question: Father is 5 times faster than son. Father completes a work in 40 days before son. If both of them work together, when will the work get complete?
(A) 8 1/0
(B) 8 1/3
(C) 8 1/8
(D) 8 1/6
(E) 8 1/5
Rationale: As efficiency is inversely proportional to days, If Father : son's efficiency is 5 : 1, then Days taken by them should be 1 : 5. Assume, the days taken by them are k, 5k.
Given that father takes 40 days less. So 5k - k = 40 ⇒⇒ k = 10
Father takes 10 days to complete the work. Total work is 10 x 5 = 50 units.
If both of them work together, they complete 5 + 1 units a day. 6/day. To complete 50 units, they take 50/6 = 8 1/3 days.
Ans: B
Answer: (B) 8 1/3
Question: Twenty four men can do a work in 42 days. How many men are required to complete the work in 21 days?
(A) 20
(B) 10
(C) 50
(D) 40
(E) 48
Rationale: E
48
We have M1 D1 = M2 D2
So, 24 * 42 = M2 * 21 => M2 = 48.
Answer is E
Answer: (E) 48
Question: Siddharth wants to borrow Rs.5000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) s.21.60
(B) s.21.68
(C) s.21.18
(D) s.21.98
(E) s.18
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.5,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 5,000{ [1 + 6/100]2 - 1 - 12/100}
= 5,000 {(1.06)2- 1 - 0.12} = 5,000(1.1236 - 1 - 0.12)
= 5,000 (0.0036) = 5 * 3.6
= Rs.18
Answer: E
Answer: (E) s.18
Question: Solve x2 â€“ 7x = 0
(A) 0,7
(B) 1,7
(C) 2,7
(D) 3,7
(E) 4,7
Rationale: This quadratic factors easily: Copyright Â© Elizabeth Stapel 2002-2011 All Rights Reserved
x2 â€“ 7x = 0
x(x â€“ 7) = 0
x = 0 or x â€“ 7 = 0
x = 0 or x = 7
The solution is x = 0, 7
ANSWER A
Answer: (A) 0,7
Question: Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 2 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
(A) 1/3
(B) 1/2
(C) 1/4
(D) 1
(E) 5/6
Rationale: A+B =2; A+C =3/2 ,B+C =2 ; ADD THEN 2*(A+B+C) = 4+3/2 = 11/2
A+B+C = 11/4 HRS
C
Answer: (C) 1/4
Question: Raffle tickets numbered consecutively from 1 through 250 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?
(A) 2/5
(B) 1/5
(C) 33/83
(D) 99/250
(E) 100/249
Rationale: SOLUTION
The number of integers from 1 to 250, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 50/250=1/5.
Answer: B
Answer: (B) 1/5
Question: Income of a company doubles after every one year. If the initial income was Rs. 4 lakhs.What would be the income after 5 years?
(A) 6.78 crores
(B) 1.28 crores
(C) 2.98 crores
(D) 3.78 crores
(E) 4.29 crores
Rationale: Income after 1 year=Rs. (4x2)lakhs
Income after 2 years= Rs. (4x2x2)lakhs
=Rs.4x4=16 lakhs
Income after 5years=Rs. (4x2^5)=Rs. 128 lakhs
=Rs. 1.28 crores
ANSWER: B
Answer: (B) 1.28 crores
Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
(A) 49
(B) 87
(C) 27
(D) 66
(E) 19
Rationale: Explanation:
Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4]
= 49
Answer: A) 49
Answer: (A) 49
Question: X and Y began business with Rs.10000 and Rs.8000 after 6 months, X advances Rs.2000 and Y advances Rs.2000 more.
At the end of the year, their profits amounted to Rs.2000 find the share of X and Y respectively.
(A) 1000,1000
(B) 900,1100
(C) 1200,800
(D) 800,1200
(E) 1100, 900
Rationale: (10*6 + 12*6):(8*6 + 10*6)
11:9
X share = 11/20 * 2000 = 1100.
Y share = 9/20 * 2000 = 900.
X and Y share respectively is 1100 , 900. Answer: E
Answer: (E) 1100, 900
Question: We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $530. How many green hats did we buy?
(A) A)36
(B) B)20
(C) C)40
(D) D)42
(E) E)44
Rationale: Let B be the number of blue hats and let G be the number of green hats.
B+G=85.
B=85-G.
6B+7G=530.
6(85-G)+7G=530.
510-6G+7G=530.
G=530-510=20.
The answer is B.
Answer: (B) B)20