mathewhe/aqua_rat huggingface dataset:
Question: Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 5 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible?
(A)  48
(B)  66
(C)  76
(D)  78
(E)  72
Rationale: Number of arrangements using 5 distinct digits = 5!
Number of arrangements in which 4 and 5 are adjacent - consider 4 and 5 together as one group. Now you have 4 numbers/groups to arrange which can be done in 4! ways. In each of these arrangements, 4 and 5 can be arranged as 45 or 54.
Number of arrangements in which 3 and 4 are not adjacent = 5! - 2*4! = 72
Answer : E
Answer: (E)  72
Question: Adding two non multiples of E always results in a multiple of E; which of the following must be the value of E ?
(A) [A] two
(B) [B] three
(C) [C] five
(D) [D] ten
(E) [E] hundred
Rationale: NON- multiples of 2 would always be ODD and sum of two odd would be EVEN.
so irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2..
A
Answer: (A) [A] two
Question: When 20 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
(A) 2 : 1
(B) 4 : 3
(C) 3 : 2
(D) Data inadequate
(E) None of these
Rationale: Let the first and the second numbers be x and y respect then
y + 20% of x = 140% of y
or, y + 0.2x = 1.4y
or, 0.2x = 0.4y
∴ x : y = 0.4 : 0.2 = 2 : 1
Answer A
Answer: (A) 2 : 1
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
(A) 8 2/3 days
(B) 9 2/3 days
(C) 10 2/3 days
(D) 10 days
(E) 11 days
Rationale: Explanation:
2/10 + 4/15 + x/20 = 1
x = 32/3 = 10 2/3
Answer: C
Answer: (C) 10 2/3 days
Question: If two students starting from same point, walking in the opposite directions with 6km/hr and 9km/hr as average speeds respectively. Then the distance between them after 4 hours is?
(A) 65 km
(B) 55km
(C) 15km
(D) 60km
(E) 75km
Rationale: Explanation:
Total distance = Distance traveled by person A+ Distance traveled by person B
= (6× 4) + (9× 4)
= 24+ 36
= 60 Km
Answer:D
Answer: (D) 60km
Question: There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that no two girls sit together?
(A) 1/12!
(B) 6!5!/12!
(C) 6!6!/12!
(D) 2∗6!6!/12!
(E) 6!7!/12!
Rationale: If girls are alternate, then only no 2 girls can be together.
So among 12 places, girls can be seated in 6 alternate places in 6! ways.
And boys can be seated in the remaining 6 places in 6! ways.
Therefore total number of ways = 6! * 6!
But there could be 2 such arrangements-->
1. When first place is filled by a girl
2. When first place is filled by a boy
Therefore total number of ways = 2*6! * 6!
Also total number of ways to fill 12 places = 12!
Hence probability =2∗6!6!/12!
Answer:D
Answer: (D) 2∗6!6!/12!
Question: How many ways can 4 friends be arranged around a circular dinner table?
(A) A)6
(B) B)48
(C) C)96
(D) D)120
(E) E)720
Rationale: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (4 - 1)! = 3! = 6.
Answer: A.
Answer: (A) A)6
Question: A lent Rs. 4000 to B for 2 years and Rs. 2000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is :
(A) 14%
(B) 15%
(C) 12%
(D) 13.75%
(E) 14.56%
Rationale: Explanation:
Let the rate of interest per annum be R%
Simple Interest for Rs.4000 for 2 years at R% + Simple Interest for Rs.2000 for 4 years at R%
= 2200
(4000×R×2)/100 + (2000×R×4)/100 = 2200
80R + 80R = 2200
160R = 2200
16R = 220
4R = 55
R = 55/4 = 13.75%
Answer: Option D
Answer: (D) 13.75%
Question: Insert the missing number. 12, 25, 49, 99, 197, 395, X
(A) 579
(B) 722
(C) 780
(D) 812
(E) 789
Rationale: Each number is twice the previous one with 1 added or subtracted alternatively.
395X2-1=789
Answer: (E) 789
Question: The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 24 kmph?
(A) 21.21
(B) 22.26
(C) 90.9
(D) 24.86
(E) 25.25
Rationale: distance covered in 1 min=(24*1000)/60=400m
circumference of the wheel=(2*(22/7)*.70)=4.4m
no of revolution per min=400/4.4=90.90
ANSWER:C
Answer: (C) 90.9
Question: How many 6 letter words are formed using the letters of the word POLICY?
(A) 129
(B) 420
(C) 750
(D) 680
(E) 720
Rationale: The number of letters in the given word is 6.
The number of 6 letter words that can be formed using these four letters is 6P6=6*5*4*3*2*1=720
Answer:E
Answer: (E) 720
Question: A marketing firm determined that, of 200 households surveyed, 80 used neither Brand W nor Brand B soap, 60 used only Brand W soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?
(A)  15
(B)  20
(C)  30
(D)  40
(E)  45
Rationale: SOLUTION FOR SOAP W AND SOAP B
(D) 40
Answer: (D)  40
Question: 12 + 13 + 14 + ... 51 + 52 + 53+ 54 = ?
(A) 1419
(B) 1362
(C) 1363
(D) 1364
(E) 1365
Rationale: Sum = 12 + 13 + 14 + ... 51 + 52 + 53 + 54
Sum of n consecutive positive integers starting from 1 is given as n(n+1)/2
Sum of first 54 positive integers = 55*54/2
Sum of first 11 positive integers = 11*12/2
Sum = 12 + 13 + 14 + ... 51 + 52 + 53 + 54 = 55*54/2 - 11*12/2 = 1419
Answer : A
Answer: (A) 1419
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50
(B) 87
(C) 52
(D) 76
(E) 21
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
Answer: (A) 50
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 55
(B) 58
(C) 64
(D) 65
(E) 70
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: a = 5^15 - 125^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: This is a tricky worded question and I think the answer is should be D not C...
Here is my reason :
The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime
Number has no factor grater than 1 and Itself .
On the other hand the stem says that X COULD get how many different number NOT MUST get different number ( this is very important issue )
AS our friends say, if we simplify Numerator more we can obtain : 5^12 ( 5^3-1) = 5^12 (124) = 5^12 (31*2*2) divided by x and we are told that this fraction is
An integer . so, X COULD Be ( not Must be) 5 , 31 ,or 2 !!! so , X could get none different values and answer is A....
Answer: (A) None
Question: If n is an integer greater than 6, which of the following must be divisible by 11 ?
(A) n(n + 5)(n – 6)
(B) n(n + 4)(n – 2)
(C) n(n + 3)(n – 5)
(D) n(n + 1)(n – 4)
(E) n(n + 2)(n – 1)
Rationale: If we assume n as being either 7 , 8 or 9 we can easily see why A is the correct answer .. Because in every instance , either of the 3 numbers multiplied will be divisible by 3 and the entire product will meet the requirements..
if n =10 , then n +1 is divisible by 11...
D
Answer: (D) n(n + 1)(n – 4)
Question: Set I consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set I, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: I = {3,-8,Y,19,-6}
B = {k,-3,0,16,-5,9}
Y > 21
So L = Median of I = 3
M = Mode of Set B
Z = (3)^M
If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor
=> M = 0
Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B.
Answer - C
Answer: (C) 0
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x
(A) 2345
(B) 3245
(C) 3457
(D) 5688
(E) 3158
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
E
Answer: (E) 3158
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
(A) 2
(B) 1
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.
So, B joined for 8 months.
Answer: D) 8 months
Answer: (D) 8
Question: 14 is what percent of 70?
(A) 0.2%
(B) 2%
(C) 5%
(D) 20%
(E) 500%
Rationale: 14= x*70/100
x = 20%
Ans; D
Answer: (D) 20%
Question: How many integers between 100 and 300 are there such that their unit digit is odd?
(A) 100
(B) 120
(C) 200
(D) 50
(E) 150
Rationale: 200 numbers between - 100 and 300
Out of which half would be even, half odd.
Number of odd unit digit number = 100.
correct option is A
Answer: (A) 100
Question: A train starts from Delhi at 6.00 a.m. and reaches Meerut at 10 a.m. The other train starts from Meerut at 8 a.m. and reaches Delhi at 11.30 a.m. If the distance between Delhi and Meerut is 200 km, then at what time did the two trains meet each other?
(A) 8.56 a.m
(B) 8.46 a.m
(C) 7.56 a.m
(D) 8.30 a.m
(E) None of these
Rationale: The Speed of the train starting from Delhi = 200/4 = 50 km/h
The Speed of train starting from Meerut = 200/3.5 = 400/7 km/h
Suppose the two trains meet x hours after 6.00 am
Then x X 50 + (x - 2) x 400/7 = 200
or, 350x + 400x - 800 = 1400
or, 750x = 2200
or, x = 2200/750 = 2h 56 min
Hence, the required time = 8.56 am
ANSWER:A
Answer: (A) 8.56 a.m
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 32
(B) 28
(C) 29
(D) 54
(E) 20
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x
= 20 km.
Answer:E
Answer: (E) 20
Question: Jacob is 10 years old. He is 5 times as old as his brother. How old will Jacob be when he is twice as old?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: j=10;
j=5b;
b=10/5=2;
twice as old so b=2(now)+(2)=4;
jacob is 10+4=14
ANSWER:B
Answer: (B) 14
Question: There are ten houses on the street. Three people live in each house. How many people live on the street?
(A) 20
(B) 25
(C) 30
(D) 32
(E) 9
Rationale: Ans is :C, 30 because 10 x 3 = 30.
Answer: (C) 30
Question: On the shelf, there are three books of poetry, five novels, and eight reference works. Suppose we picked two books at random. What is the probability that we pick one novel and one reference work?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: We could pick one novel and then one reference work, or, we could choose one reference work and then one novel.
P(one novel and one reference work) = 5/16*8/15 + 8/16*5/15 = 1/3
The answer is B.
Answer: (B) 1/3
Question: Sum of the consequent 7 integers equals 1617. Find the no. of prime numbers in that sequence.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let the numbers be x, x+1, x+2, x+3, x+4, x+5, x+6
Since their sum equals 1617, we have-
x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6)=1617
7x+21=1617
7x=1596
x=228
Hence the numbers are: 228,229,230,231,234,235,236
Prime Numbers: 229, 231
ANSWER:B
Answer: (B) 2
Question: To gain profit, a milkman adds 1.5 litre of water to a certain amount of milk. He sells the adulterated milk at Rs.28 per litre and pure milk costs Rs.36 per litre. Find the amount of milk.
(A) 5.25
(B) 5.27
(C) 5.22
(D) 5.21
(E) 5.29
Rationale: Explanation:
Let the amount of milk be x.
36x = 28(x + 1.5)
36x = 28x + 42
8x = 42
x = 5.25 litres
ANSWER:A
Answer: (A) 5.25
Question: How many pieces of 85 cm length can be cut from a rod of 25.5 meters long?
(A) 50
(B) 40
(C) 30
(D) 20
(E) 10
Rationale: Number of pieces = 2550/85 = 30
The answer is C.
Answer: (C) 30
Question: Matt and Peter can do together a piece of work in 24 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately.
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: Together they complete the job in 24 days means they complete 12/24 of the job after 12 days.
Peter completes the remaining (12/24) of the job in 10 days which means that the whole job(1) can be completed in X days.
X=12/(12/24)=24
A
Answer: (A) 24
Question: The tank contains 16 Fishes. 5 of the fishes are shark, 6 are jelly fishes, and 5 are gold fishes. If two fishes are randomly selected from the tank, one after the other, what is the probability that both will be jelly fishes?
(A) 2/8
(B) 1/8
(C) 1/6
(D) 2/7
(E) 8/7
Rationale: Probability of getting the first Jelly Fish - 6/16
Probability of getting the second Jelly Fish - 5/15
total probability = 6/16*5/15 = 1/8
correct option B
Answer: (B) 1/8
Question: P can do a work in 15days and Q cando the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
(A) 6/15
(B) 7/13
(C) 8/15
(D) 9/17
(E) 2/13
Rationale: Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
C
Answer: (C) 8/15
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 22
(B) 20
(C) 288
(D) 277
(E) 12
Rationale: C = 1/2 - 1/4 - 1/5 = 1/20 => 20 days
Answer: B
Answer: (B) 20
Question: If f(a)=2a+6, what is the value of (f(2a)+f(a)) ?
(A) 2a-4
(B) 8a-7
(C) 9a+5
(D) 6a+12
(E) 3a+5
Rationale: f(a)=2a+6
f(2a)= 4a+6
(f(2a)+f(a)) = 4a+6+2a+6 = 6a+12
Answer is D
Answer: (D) 6a+12
Question: Two dishonest shop-owners mix water to milk before selling it in the market. The first shop-owner mixes
water to milk in the ratio 2 : 1 and second shop-owner mixes water to milk in the ratio 3 : 1. Now if both
of them sell the milk at their cost price of $.60 and $.80 respectively, then from which shop-owner should the customer purchase the milk to get the maximum quantity of pure milk per $ paid?
(A) 1st milkman
(B) 2nd milkman
(C) Any one
(D) Data Inadequate
(E) none of above
Rationale: Milkman 1 ratio of W:M = 2:1
hence milk = 1/3*0.6 = 0.2 = 33.33%
Milkman 2 W:M = 3:1
milk = 1/4*0.8 = 0.2 = 16.666%
Hence A.
Answer: (A) 1st milkman
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.6 sec
(B) 18.8 sec
(C) 14.8 sec
(D) 10.8 sec
(E) 11.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
Answer: D
Answer: (D) 10.8 sec
Question: 21 goats eat as much as 15 cows. How many goats eat as much as 35 cows?
(A) 49
(B) 32
(C) 36
(D) 41
(E) 45
Rationale: Explanation:
15 cows ≡ 21 goats
1 cow ≡ 21/15 goats
35 cows ≡ 21×35/15 goats
≡ 21×7/3 goats
≡ 7 × 7 goats
≡ 49 goats
Answer: Option A
Answer: (A) 49
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 2/5 % his yearly income diminishes by Rs.61.50. his capital is
(A) 223.78
(B) 37.78
(C) 246.0
(D) 278.88
(E) 102.5
Rationale: Explanation:
Capital = Rs.x , then
3/5x =61.5
x = 102.50
Answer: E) Rs.102.50
Answer: (E) 102.5
Question: How many words can be formed by using all letters of the word ‘RIO’ ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Solution
The word RIO contains 3 different letters.
Required number of words = 3P3 = 3 ! = (3 x 2 x 1) = 6
Answer A
Answer: (A) 6
Question: What is the twenty-third decimal to the right in the fraction 23/24?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Multiply the numerator with 10, which gives
=> 230/24 = 115/12 = 9.58333..
This shows that the number 3 is repeating and hence the 23rd decimal.
You may divide the result with 10, yielding 0.983333.., which is the correct result for 23/24.
ANSWER:A
Answer: (A) 1
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 3 years and that for 9 years?
(A) 1 : 3
(B) 2 : 3
(C) 1 : 2
(D) 3 : 2
(E) 1 : 4
Rationale: Let the principal be P and rate of interest be R%.
Required ratio =
(P x R x 3)/100 DIVIDED BY	(P x R x 9)/100
=	3PR/9PR	=	3/9	= 1 : 3.
ANSWER : A
Answer: (A) 1 : 3
Question: for which value of n, 4^85+2^3373+4^n will be the perfect square ??
(A) 1878
(B) 1978
(C) 1578
(D) 2578
(E) 3287
Rationale: given expression is in the form of a^2+2ab+b^2
4^85=2^2(85)
4^n=2^2n
2^3373=2*2^85*2^n
3373=85+1+n
n=3373-86=3287
ANSWER:E
Answer: (E) 3287
Question: A driver goes on a trip of 60 kilometers, the first 30 kilometers at 48 kilometers per hour and the remaining distance at 24 kilometers per hour. What is the average speed of the entire trip in kilometers per hour?
(A) 30
(B) 32
(C) 36
(D) 40
(E) 42
Rationale: The time for the first part of the trip was 30/48 = 5/8 hours.
The time for the second part of the trip was 30/24 = 5/4 hours.
The total time fro the trip was 5/8 + 5/4 = 15/8 hours.
The average speed for the trip was 60 / (15/8) = 32 kph
The answer is B.
Answer: (B) 32
Question: Eight cards numbered from 1 to 8 are placed in an empty bowl. First one card is drawn and then put back into the bowl, and then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 4?
(A) 1/5
(B) 2/5
(C) 1/7
(D) 2/7
(E) 3/7
Rationale: There are 7 ways to get a total sum of 10.
2 of these ways include the number 4.
The probability that one of the cards is a 4 is 2/7
The answer is D.
Answer: (D) 2/7
Question: A train passes a station platform in 32 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) 123
(B) 166
(C) 240
(D) 157
(E) 180
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, (x + 300) / 32 = 15
x + 300 = 480
x = 180 m.
Answer: E
Answer: (E) 180
Question: 8k8
+ k88
--------
1,6e6
If k and e represent non-zero digits within the integers above, what is e?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 17
Rationale: 8k8
k88
--------
16e6
Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and e=6.
Answer: A.
Answer: (A) 6
Question: in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 7 people all together .how many people can sit in a bus?
(A) 52
(B) 49
(C) 95
(D) 88
(E) 66
Rationale: Right Side =15 seat
Left Side =15-3 (3 few seat in right side)= 12 seat
Total= 15+12= 27
People can seat in 27 seat= 27*3=81
People can seat in Last Seat = 7
Total People can seat= 81+7=88
ANSWER:D
Answer: (D) 88
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 24 minutes. The waste pipe can empty the full cistern in?
(A) 8 min
(B) 7 min
(C) 6 min
(D) 9 min
(E) 4 min
Rationale: 1/10 + 1/15 - 1/x
= 1/24
x = 8
Answer: C
Answer: (C) 6 min
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 30
(B) 77
(C) 25
(D) 27
(E) 12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer: A
Answer: (A) 30
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 6
(B) 5
(C) 8
(D) 9
(E) 4
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8.Answer: C
Answer: (C) 8
Question: If p is even and q is odd, which of the following is odd?
(A) pq
(B) 5pq
(C) 6(p^2)q
(D) 5p + 6q
(E) 6p + 5q
Rationale: Just checking options (In case you have difficulty then choose values of r=2 and t=1)
p = even
q= Odd
A. pq = Even*Odd = EvenINCORRECT
B. 5pq = Odd*Even*Odd = EvenINCORRECT
C. 6(pr^2)q = 6*(Even^2)*Odd = EvenINCORRECT
D. 5p + 6q = 5*Even + 6*Odd = Even+Even = EvenINCORRECT
E. 6p + 5q = 6*Even + 5*Odd = Even+Odd = OddCORRECT
Answer: option E
Answer: (E) 6p + 5q
Question: If x and y are positive integers and 20x=10y what is the least possible value of xy?
(A)  14
(B)  28
(C)  63
(D)  84
(E)  100
Rationale: 20x=10y
=> x/y = 1/2
=> 2x=y
2(3)=1(3) => x*y=9 But it is not given
2(10)=1(10) => x*y=100
E
Answer: (E)  100
Question: A hat vendor bought hats at Rs 5 per 3 hats. He sold them at Rs 10 per 4 hats. What was his profit percentage?
(A) 50
(B) 88
(C) 77
(D) 88
(E) 11
Rationale: Selling price per hat = 10/4
Profit percentage = (S.P – C.P / C.P) x 100
Substituting the above SP and CP we get 50%.
Answer:A
Answer: (A) 50
Question: A man is 32 years older than his son. In six years, his age will be twice the age of his son. The present age of this son is
(A) 26 years
(B) 27 years
(C) 28 years
(D) 29 years
(E) 30 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+32.
=> 2(x+6) = (x+32+6)
=> 2x+12 = x+38
=> x = 26 years
Answer: Option A
Answer: (A) 26 years
Question: A reduction of 15% in the price of oil enables a house wife to obtain 4kgs more for Rs.1200, what is the reduced price for kg?
(A) 43
(B) 55
(C) 35
(D) 45
(E) 40
Rationale: 1200*(15/100) = 180 ---- 4
? ---- 1 => Rs.45
Answer:D
Answer: (D) 45
Question: How many positive integers less than 255 are multiple of 4 but NOT multiples of 6?
(A) 20
(B) 31
(C) 42
(D) 43
(E) 64
Rationale: From here, it might be easier to go up in bounds of 60, so we know that 61-120 gives 10 more numbers. 121-180 and 181-240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 42, as all the other choices are very far away. The numbers 244 and 248 will come and complete the list that’s (naughty or nice) under 250. Answer choice D is correct here.
Answer: (D) 43
Question: Rice weighing 3power3/4 pounds was divided equally and placed in 4 containers. how many ounces of rice were in each?
(A) 15 ounces
(B) 25 ounces
(C) 12 ounces
(D) 22 ounces
(E) 35 ounces
Rationale: 3power3/4 / 4 pounds, = (4x3+3)/4 ponds. = (15/4) /4 ponds. = (15/4) / (1/4) ponds. = 15/16 pounds. 1 pound = 16 ounces. therefore, 15/16 pounds = 15/16*16 ounces = 15 ounces. Correct answer : (A)
Answer: (A) 15 ounces