mathewhe/aqua_rat huggingface dataset:
Question: A = {2, 3, 5, 7, 19}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
(A) 32
(B) 16
(C) 19
(D) 20
(E) 36
Rationale: Step 1: Find out the number of products you get.
5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20
Step 2: Remove the products that appear more than once.
Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.
2, 3
2, 4, 6
The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.
Answer = 20 - 1 = 32
Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.
A
Answer: (A) 32
Question: A person purchased a TV set for Rs. 1600 and a DVD player for Rs. 700 . He sold both the items together for Rs. 3500. What percentage of profit did he make?
(A) 20.12%
(B) 96.21%
(C) 52.17%
(D) 75.01%
(E) 23.00%
Rationale: The total CP = Rs. 1600 + Rs. 700
= Rs. 2300 and SP = Rs. 3500
Profit(%)
= (3500 - 2300)/2300 * 100
= 52.17%
Answer: C
Answer: (C) 52.17%
Question: Find three consecutive odd integers so that the sum of twice the first, the second
and three times the third is 152.
(A) 20,23,25
(B) 23,25,27
(C) 25,28,31
(D) 30,33,35
(E) 29,31,35
Rationale: First x Make the first x
Second x+2 Odd numbers sowe add 2(same as even!)
Third x+4 Add 2more (4 total) to get the third
2F +S +3T =152 Twicethefirstgives2F andthree times thethirdgives3T
2(x)+(x+2)+3(x+4)=152 Replace F , S, and T withwhatwe labled them
2x+x+2+3x+12=152 Distirbute through parenthesis
6x+14=152 Combine like terms 2x+x+3x and 2+14
−14 −14 Subtract 14 fromboth sides
6x=138 Variable ismultiplied by 6
6 6 Divide both sides by 6
x=23 Our solution for x
First 23 Replace xwith 23 in the original list
Second (23)+2=25 The numbers are 23, 25, and 27
Third (23)+4=27
correct answer B
Answer: (B) 23,25,27
Question: A girl borrows 65000 for 5 years at 5% p.a. simple interest. she immediately lends it to another person at 9 % p.a. for 5 years. Find her gain in the transaction per year.
(A) 2600
(B) 2500
(C) 2550
(D) 2650
(E) 3600
Rationale: Gain in 5 years
= [(65000Ã—9Ã—5/100)âˆ’(65000Ã—5Ã—5/100)]
= (29250 â€“ 16250) = 13000.
âˆ´ Gain in 1 year = (13000â„5) = 2600
Answer A
Answer: (A) 2600
Question: A man walks from B to C, a distance of x miles, at 15 miles per hour and returns at 12 miles per hour. What is his average speed?
(A) 10 mph
(B) 13 mph
(C) 12 mph
(D) 13.3 mph
(E) 14 mph
Rationale: Total distance covered = 2x
Time taken12miles / hour = x/12 hrs
Time taken @ 15 miles / hour = x/10 hrs
Avg speed = 2x / (x/15 + x/12) = 13.3 mph
Ans is D
Answer: (D) 13.3 mph
Question: The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 6 seconds than it was moving after 3 seconds?
(A) 4
(B) 9
(C) 15
(D) 48
(E) 33
Rationale: Given: z=s^2+2s for 0≤s≤7
z(3) = 3^2 + 2*3 = 15
z(6) = 6^2 + 2*6 = 48
Therefore z(7) - z(3) = 48 - 15 = 33 km/hr
Option E
Answer: (E) 33
Question: Johnny borrows $30,000 from Tony at 2% daily interest compounded daily. How much does Johnny owe Tony after 8 weeks?
(A) 30000*0.02^56
(B) 30000*1.12
(C) 30000*2.12
(D) 30000*1.02^56
(E) (30000*1.02)^56
Rationale: A=A= P(1+r100)^n
So, A=30000(1+2/100)^7∗8
So, A=A= 30000(1.02)^56
Hence answer will be (D)
Answer: (D) 30000*1.02^56
Question: A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole ?
(A) 150 m
(B) 200 m
(C) 125 m
(D) 115 m
(E) None
Rationale: Answer
∵ 8 m shadow means original height = 12 m
∴ 1 m shadow means original height = 12/8 m
∴ 100 m shadow means original height = (12/8) x 100 m
= (6/4) x 100 = 6 x 25 = 150 m
Correct Option: A
Answer: (A) 150 m
Question: At what rate percent per annum will a sum of money double in 16years?
(A) 10.6%
(B) 3.65%
(C) 6.25%
(D) 8.32%
(E) 11%
Rationale: Let principle = P
S.I. = P
T = 16yrs
Rate = 100*P/P*16 = 25/4% = 6.25%
Answer is C
Answer: (C) 6.25%
Question: The organizers of a week-long fair have hired exactly six security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?
(A) 7
(B) 6
(C) 5
(D) 3
(E) 2
Rationale: For any given day, only the guards patrolling on the previous day won't be available. So, 2 guards who patrolled on Friday won't be available. We are thus left with 4 guards.
To choose 2 out of 4, we will have 4C2 = 6 different pairs.
The answer is B.
Answer: (B) 6
Question: The sum of even numbers between 1 and 31 is:
(A) 240
(B) 789
(C) 520
(D) 879
(E) 456
Rationale: Explanation:
Let Sn = (2 + 4 + 6 + ... + 30). This is an A.P. in which a = 2, d = 2 and l = 30
Let the number of terms be n. Then
a + (n - 1)d = 30
=>2 + (n - 1) x 2 = 30
n = 15.
Sn =	n/2(a + l)=15/2	x(2 + 30) = (15 x 16) = 240.
ANSWER:A
Answer: (A) 240
Question: The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length W of a cube whose surface area is equal to 6z?
(A) W=16
(B) W=8√2
(C) W=8
(D) W=2√2
(E) (√2)/3
Rationale: 800 score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.
The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , oranswer choice (D).
Answer: (D) W=2√2
Question: In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?
(A) 1/20
(B) 1/10
(C) 1/5
(D) 2/5
(E) 3/4
Rationale: In this corporation, there are 400 total employees. There are 100 women. Of the 300 men, 20% have advanced degrees —-10% of 300 must be 30, so 20% of 300 must be 60. Add the women and the men with advanced degrees: 100 + 60 = 160. This is the OR region, full set of individuals that satisfy the condition “has an advanced degree or is female.” Of the 400 employees, what’s the probability of picking one of the 160 in this particular group?
P = 160/400 = 16/40 = 4/10 = 2/5
Answer = D
Answer: (D) 2/5
Question: The ratio between the speeds of two trains is 5: 7. If the second train runs 840 kms in 6 hours, then the speed of the first train is ?
(A) 90 km/hr
(B) 120 km/hr
(C) 100 km/hr
(D) 110 km/hr
(E) None of these
Rationale: Explanation:
Let the speeds of two trains be 5X and 7X km/hr.
7/X=840/6=>X=20Km/hr
So speed of first train is 20*5 = 100 km/hr
Option C
Answer: (C) 100 km/hr
Question: A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?
(A) 100
(B) 114
(C) 126
(D) 154
(E) 157
Rationale: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
\inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126
C
Answer: (C) 126
Question: Excluding the stoppages, the speed of a bus is 32 km/hr and including the stoppages the speed of the bus is 16 km/hr. For how many minutes does the bus stop per hour?
(A) 15 min
(B) 10 min
(C) 12 min
(D) 30 min
(E) 18 min
Rationale: Speed of the bus without stoppage=32 km/hr
Speed of the bus with stoppage=16km/hr
Difference in speed=16 km/hr
so,the time taken in the stoppages = time taken to cover 16 km=(16/32)hr = 1/2 hr =30 min
ANSWER:D
Answer: (D) 30 min
Question: From the given equation find the value of c: cÂ²-3c-10
(A) 1
(B) 3
(C) 5
(D) 2
(E) -5
Rationale: (c - 5)(c + 2)
C = -2 or 5
Answer is C
Answer: (C) 5
Question: Walking at 5/6th of its usual speed a cab is 5mnts late. Find its usual time to cover the journey?
(A) 25m
(B) 45m
(C) 32m
(D) 50m
(E) 62m
Rationale: New speed = 5/6th of usual speed
New time = 6/5th of usual time
6/5 UT - UT = 5m
UT/5 = 5m
UT = 25m
Answer is A
Answer: (A) 25m
Question: A fair coin is tossed repeatedly. If heads appears on first 6 tosses what is the probability that tail appears on the next two tosses?
(A) 1/6
(B) 1/5
(C) 1/3
(D) 1/4
(E) 1/6
Rationale: Explanation :
Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.
1/2 * 1/2 = 1/4
Answer : D
Answer: (D) 1/4
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 18 kmph and 48 kmph. After how much time will they meet for the first time at the starting point?
(A) 120 sec
(B) 176 sec
(C) 360 sec
(D) 187 sec
(E) 189 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (18 * 5/18) , 600/ (48 * 5 /18) }
= 360 sec.
Answer: C
Answer: (C) 360 sec
Question: If 6 and 8 are factors of 60n, what is the minimum value of n?
(A)  2
(B)  4
(C)  7
(D)  14
(E)  56
Rationale: 60n/6*8 should be integer => 2*2*3*5*n/2*3*2*2*2 = 5*n/4 must be an integer
for this to be true n must multiple of 4, thus min of n = 4
hence B
Answer: (B)  4
Question: How many 3-digit numerals begin with a digit that represents a prime and end with a digit that represents a odd prime number?
(A) 16
(B) 120
(C) 160
(D) 180
(E) 240
Rationale: prime digits 2,3,5 and 7.
three digit numbers _ _ _
1st place can be filled in 4 ways
2nd place can be filled in 10 ways
3rd place can be filled in 3 ways
Total=4*10*3=120
Ans : B
Answer: (B) 120
Question: If a - b = 6 and a2 + b2 = 50, find the value of ab.
(A) A)7
(B) B)12
(C) C)15
(D) D)18
(E) E)20
Rationale: Explanation:
2ab = (a2 + b2) - (a - b)2
= 50 - 36 = 14
ab = 7.
Answer: A
Answer: (A) A)7
Question: There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'S', then how many triangles can be determined with the 15 points that contain the point S?
(A) 91
(B) 105
(C) 182
(D) 210
(E) 455
Rationale: Fist point is S which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2=C
Answer: (C) 182
Question: If a:b=5:6 and b:c=2:3 find a:b:c?
(A) 6:5:9
(B) 5:9:3
(C) 9:5:6
(D) 5:9:6
(E) 5:6:9
Rationale: a:b = 5:6, b:c = 2:3
5:6
2:3
(a = a × b, b = b × b and c = b × c)
a:b:c = 5:6:9
E
Answer: (E) 5:6:9
Question: A train running at the speed of 50 km/hr crosses a post in 4 seconds. What is the length of the train?
(A) 90
(B) 120
(C) 60
(D) 95
(E) 75
Rationale: Speed=(54x5/18)=15 m/sec.
Length of the train=(Speed x Time).
Length of the train=15x4m=60m.
Answer: C
Answer: (C) 60
Question: A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
(A) 8 days
(B) 10 days
(C) 15 days
(D) 11 3/7 days
(E) None of these
Rationale: Explanation:
(x â€“ 5)/15 + x/20 = 1
x = 11 3/7 days
ANSWER IS D
Answer: (D) 11 3/7 days
Question: If log 2 = 0.30103, the number of digits in 520 is
(A) 14
(B) 16
(C) 18
(D) 25
(E) 26
Rationale: Solution
Log 520	=20 log 5
=20 ×[log(10/2)]
=20 (log 10 - log 2)
=20 (1 - 0.3010)
=20×0.6990
=13.9800.
Characteristics	= 13.
Hence, the number of digits in Log 5(20) is 14.
Answer A
Answer: (A) 14
Question: 60 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?
(A) 80 litres
(B) 90 litres
(C) 120 litres
(D) 170 litres
(E) None of these
Rationale: Explanatory Answer
To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*60 = 80 litres.
However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.
i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.
Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*80 = 120 litres.
Answer C
Answer: (C) 120 litres
Question: If 2^z is a factor of 26!, which of the following could be the value of z?
I. 22
II. 23
III. 24
(A) I ​ only
(B) II only
(C) I​ and II
(D) I, II, and III
(E) None
Rationale: 26! contains all numbers from 1 to 26. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.
Multiples of 2 = 13
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 23
The answer is C.
Answer: (C) I​ and II
Question: Find the missing number
5 : 24 :: 8 : ?
(A) 61
(B) 62
(C) 63
(D) 64
(E) 65
Rationale: 5^2 -1= 24
so 8^2 -1 =63
ANSWER:C
Answer: (C) 63
Question: What should be the least number to be added to the 3198 number to make it divisible by 8?
(A) 12
(B) 17
(C) 2
(D) 77
(E) 26
Rationale: Answer : 2
Option : C
Answer: (C) 2
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 292 runs?
(A) 6.5
(B) 6.22
(C) 6.29
(D) 6.39
(E) 6.13
Rationale: Required run rate
= [292 - (3.2 * 10)]/40
= 260/40
= 6.5
Answer: A
Answer: (A) 6.5
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) Rs. 650
(B) Rs. 690
(C) Rs. 698
(D) Rs. 700
(E) Rs. 740
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
Answer: (C) Rs. 698
Question: In how many years will a sum of money doubles itself at 25% per annum on simple interest?
(A) 4%
(B) 8%
(C) 10%
(D) 12%
(E) 15%
Rationale: P = (P*25*R)/100
R = 4%
Answer:A
Answer: (A) 4%
Question: Entry fee in an exhibition was Rs. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is :
(A) 33
(B) 37
(C) 60
(D) 28
(E) 27
Rationale: Explanation:
Let the total original sale be Rs. 100. Then, original number of visitors = 100.
New number of visitors = 120/0.75 = 160.
Increase % = 60 %.
Answer: C) 60 %
Answer: (C) 60
Question: If 8 persons can do 8 times of a particular work in 8 days, then, 9 persons can do 9 times of that work in?
(A) 3 days
(B) 4 days
(C) 6 days
(D) 7 days
(E) 8 days
Rationale: That is, 1 person can do one time of the work in 8 days.
Therefore, 9 persons can do 9 times work in the same 8 days itself
E)
Answer: (E) 8 days
Question: Consider two statements
Statement 1 => If R is an integer and R=2p+1 where p is not an integer.
Statement 2 => If S is an integer and S=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of R and S respectively
(A) 1) Odd,Even
(B) 2) Odd,Odd
(C) 3) Even,Odd
(D) 4) Even,Even
(E) 5) Cannot be determined
Rationale: answer will be E
R = integer
R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even R would odd
if n odd R would be even
ANSWER IS E
Answer: (E) 5) Cannot be determined
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
(A) 1/4
(B) 1/5
(C) 2/5
(D) 3/5
(E) 3/7
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.
C)
Answer: (C) 2/5
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is -
(A) 8/13
(B) 6/13
(C) 3/13
(D) 4/13
(E) 1/13
Rationale: Explanation:
P(Sá´œK) = P(S) + P(K) - P(Sâˆ©K), where S denotes spade and K denotes king.
P(Sá´œK) = 13/52 + 4/52 - 1/52 = 4/13
Answer: D
Answer: (D) 4/13
Question: Ben
ips a fair coin repeatedly. Given that Ben's first coin
ip is heads, compute the probability
Ben
ips two heads in a row before Ben
ips two tails in a row.
(A) 2/3
(B) 3/3
(C) 1/3
(D) 1/1
(E) 2/2
Rationale: If Ben successfully
ips two heads in a row, then Ben must have
ipped the coin an
even number of times. If Ben successfully
ips two tails in a row, then he must have
ipped
the coin an odd number of times. However, the coin must have been
ipped at least twice. The
desired probability is therefore
(1/3)/(1/2)=2/3
correct answer A
Answer: (A) 2/3
Question: Suppose 5 monkeys take 5 minutes to eat 5 bananas. How many monkeys would it take to eat 15 bananas in 15 minutes?
(A) 9
(B) 10
(C) 11
(D) 5
(E) 13
Rationale: One monkey takes 5 min to eat 1 banana , so in 15 mins 1 monkey will eat 3 bananas , so for 15 bananas in 15 min we need 15/3 =5 monkeys
ANSWER:D
Answer: (D) 5
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.6 the sixth number is?
(A) 11.4
(B) 11.3
(C) 11.8
(D) 11.5
(E) 12.7
Rationale: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.6 = 69.6
63 + 69.6 = 132.6 – 119.9 = 12.7
6th number = 12.7
Answer: E
Answer: (E) 12.7
Question: A cask is filled with alcohol and water in the ratio 5”3 Sixteen gallons of this are drawn off and the cask is filled with water and then the proportion of alcohol to water becomes 3:5 How many gallons does the cask hold ?
(A) 32
(B) 36
(C) 38
(D) 40
(E) 42
Rationale: ratio of alcohal and water is 25:15
Initially when Sixteen gallons of this are drawn off
ratio of alcohal and water is 15:9
and the cask is filled with water 15:25 which is 3:5
ANSWER:D
Answer: (D) 40
Question: The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.7 kg. the weight of the new student is ?
(A) 10.6 kg
(B) 10.8 kg
(C) 11 kg
(D) 14.9 kg
(E) None
Rationale: Answer
Weight of new student = Total weight of all 20 students - Total weight of initial 19 students
= (20 x 14.7 - 19 x 15) kg
= 9 kg.
Correct Option: E
Answer: (E) None
Question: There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men?
(A) 1932
(B) 1933
(C) 1934
(D) 1935
(E) 1936
Rationale: (5c3*11c3)+(5c4*11c2)+(5c5*11c1)
1936
ANSWER:E
Answer: (E) 1936
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 22 years. The present age of the husband is
(A) 40
(B) 36
(C) 45
(D) 55
(E) 65
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) years = 90 years.
Sum of the present ages of wife and child = (22 * 2 + 5 * 2) years = 54 years.
Husband's present age = (90 - 54) years = 36 years
Option B
Answer: (B) 36
Question: Sand is poured into a box so that the box is being filled at the rate of 3 cubic feet per hour. If the empty rectangular box is 5 feet long, 4 feet wide, and 3 feet deep, approximately how many hours does it take to fill the box?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: The volume the box is: length*width*depth = 5*4*3= 60 cubic feet.
60 cubic feet / 3 cubic feet per hour = 20 hours.
It will take 20 hours to fill the box.
The answer is D.
Answer: (D) 20
Question: The present worth of a certain sum due sometime hence is Rs. 3400 and the true discount is Rs. 340. The banker's gain is:
(A) Rs. 21
(B) Rs. 17
(C) Rs. 18
(D) Rs. 34
(E) None of these
Rationale: Explanation :
BG = (TD)2/PW=(340)2/3400=340 × 340/3400 = 340/10 = Rs. 34 Answer : Option D
Answer: (D) Rs. 34
Question: A woman complete a journey in 5 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
(A) 334 km.
(B) 216 km.
(C) 112 km.
(D) 224 km.
(E) 544 km.
Rationale: 0.5x/21 + 0.5x/24 = 5
--> x/21 + x/24 = 10
--> x = 112 km.
C
Answer: (C) 112 km.
Question: 10, 25, 45, 54, 60, 75, 80
(A) 10
(B) 45
(C) 49
(D) 54
(E) 75
Rationale: Each of the numbers except 54 is multiple of 5.
answer : C
Answer: (C) 49
Question: P and Q are the only two applicants qualified for a short-term research project that pays 480 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?
(A) $5
(B) $8
(C) $11
(D) $14
(E) $17
Rationale: Let Q's hourly wage be x, then P's hourly wage is 1.5x
Let T be the number of hours that Q needs, then P needs T-10 hours to do the job.
Since they both are paid an equal total amount of $480:
x*T=1.5x*(T-10)
T = 30 hours and Q's hourly wage is 480/30 = $16
P's hourly wage is 480/(T-10) = $24 which is $8 per hour more.
The answer is B.
Answer: (B) $8
Question: A semicircular shaped window has diameter of 63cm. Its perimeter equals
(A) 162
(B) 766
(C) 298
(D) 277
(E) 198
Rationale: Explanation:
perimeter of window = {\color{Blue} \Pi }r+2r
= [{(22/7) * (63/2)} +63]
= 99+63
= 162 cm
Answer: A) 162
Answer: (A) 162
Question: Among 700people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
(A) 20
(B) 60
(C) 80
(D) 186
(E) 210
Rationale: 56%+44%-30%=70% who like either Strawberry, Apple, or both.
That means 100%-70% = 30% do not like either Apple of Strawberry jam.
30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)
E
Answer: (E) 210
Question: Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 0.5. What value is exactly 2 standard deviations less than the mean?
(A)  10.5
(B)  11
(C)  11.5
(D)  12
(E)  12.5
Rationale: The value which is exactly two SD below the mean is: mean-2*SD=13.5-2*0.5=12.5.
Answer: E.
Answer: (E)  12.5
Question: The average age of the mother and her six children is 10 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
(A) 40
(B) 41
(C) 42
(D) 43
(E) 44
Rationale: Total age of mother and 6 children = avg x n = 10 x (6+1)= 70
If mother is excluded new average is (10 - 5) = 5
so for 6 children = 6 x 5 =30
so mother's age is 70 - 30 =40
Answer: Option A
Answer: (A) 40