mathewhe/aqua_rat huggingface dataset:
Question: Two water bottles are in side-by-side. One bottle, which is 25 inches tall, casts a shadow that is 50
inches long. The other bottle is 30 inches tall. Compute, in inches, the length of the shadow that
the taller bottle casts.
(A) 35
(B) 25
(C) 40
(D) 50
(E) 60
Rationale: The ratio of shadow to height is constant, so if x is the length of the shadow, then
25/50 = 30/x and x = 60 .
correct answer E
Answer: (E) 60
Question: 15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours. Then how many sugar cubes of 5 grams each, will 20 ants move in 3 hours?
(A) 360
(B) 480
(C) 720
(D) 960
(E) 1000
Rationale: D
15 ants move 600/5=120 sugar cubes of 10 grams in 1 hour.
5 grams sugar cubes will take less time to move.
Thus if weight of the sugar cube is 5 grams, 15 ants will move 120 X 10 / 5 = 240 sugar cubes in 1 hour.
More ants, more sugar cubes they can move.
20 ants will move 240 X 20 / 15 = 320 sugar cubes in 1 hour
Thus in 3 hours, 20 ants will move 320 X 3 = 960 sugar cubes of 5 grams.
Answer: (D) 960
Question: If w/x = 5/7 and w/y = 4/7, then (x + y)/y =
(A) 1/2
(B) 7/3
(C) 6/7
(D) 1/5
(E) 11/13
Rationale: Ratio 1:
7w = 5x
Ratio 2:
7w = 4y
5x = 4y
x= 4y/3
(x+y)/y = ((4y/3)+y)/y = y(4/3 +1)/y = 7/3
Answer is B
Answer: (B) 7/3
Question: Which from the options has the highest value?
(A) A)23/77
(B) B)23/78
(C) C)23/84
(D) D)23/87
(E) E)23/43
Rationale: 23/43.
Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator.
Answer (E).
Answer: (E) E)23/43
Question: The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.8 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 14.8 - 19 x 15) kg
= 11 kg.
Correct Option: C
Answer: (C) 11 kg
Question: How many three-digit integers between 310 and 400, exclusive, are divisible by 3 when the ones digit and the hundered digit are switched?
(A) 3
(B) 19
(C) 22
(D) 30
(E) 90
Rationale: Answer is 30
No of digits between 310 and 400 (exclusive) = 400-310-1 = 89
No Intergers divisble by 3 =~ 89/3 ~ 30
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and ones digits are switched.
e.g 372 is divisble by 3 (becae 3+7+2= 12 (divisble by 3))
switch digits 732 also divisble by 3 (becae 7+3+2= 12 (divisble by 3))
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and ones digits are switched.
You have right. So it is enough to proceed like usual to find the numbers in a given range that are divisible by 3. So 399-312/3 +1 =30.
Answer : D
Answer: (D) 30
Question: An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 62 percent of the votes cast?
(A) 75%
(B) 58%
(C) 42%
(D) 34%
(E) 25.83%
Rationale: Total Number of members = 1260
Number of members that cast votes = 525
Since , winning candidate received 62 percent of the votes cast
Number of votes for winning candidate = (62/100)*525 = 325.5
Percent of total membership that voted for winning candidate = (325.5/1260)*100 = 25.83%
Answer E
Answer: (E) 25.83%
Question: A crate measures 2 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: We can find the radius of all the three cases of cylinders.
The only crux to find the answer faster is that:
Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.
So r=2 for the surface 8*12 face.
Volume = 8pi
Answer A
Answer: (A) 2
Question: If 4<(7-x)/2, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive
(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: 12<7-x
x<-5
x+5<0
1.5<x...not possible
2.True.....Check for values x=-6,-7,-8....... etc
3.True.. Since x+5<0 -(x+5) will always be positive
Hence, Ans is B..
Answer: (B) III only
Question: If 9 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
(A) 41
(B) 42
(C) 36
(D) 44
(E) 45
Rationale: n(n-1)/2 =9*8/2
=36
ANSWER:C
Answer: (C) 36
Question: If a and b are positive integers and (2^a)^b = 2^2, what is the value of 2^a*2^b?
(A) 8
(B) 4
(C) 16
(D) 32
(E) 64
Rationale: 2^ab =2^2 therefore ab=2 either a=1or2 or b=2 or 1
therefore 2^a* 2^b = 2^(a+b)= 2^3 =8
A
Answer: (A) 8
Question: Dan's age after 20 years will be 7 times his age 4 years ago. What is the present age of Dan?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Let Dan's present age be x.
x+20 = 7(x-4)
6x = 48
x = 8
The answer is B.
Answer: (B) 8
Question: Marge has Q candies, where Q is an integer such that 20 < Q< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: If Marge divides the candies equally among 5 children, she will have 2 candies remaining.
This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47
If she divides the candies among 6 children, she will have 1 candy remaining.
this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49
ONLY 37 is common, so candies are 37 in number..
if 37 is divided in 7 kids, remainder Q= 2
C
Answer: (C)  2
Question: Find the compound ratio of (2:3), (5:3) and (2:5) is
(A) 1:2
(B) 2:3
(C) 3:4
(D) 4:9
(E) 3:2
Rationale: Required ratio = 2/3 * 5/3 * 2/5 = 4/9 = 4:9
Answer is D
Answer: (D) 4:9
Question: The average weight of 8 persons increases by 3 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
(A) 75 kg
(B) 65 kg
(C) 55 kg
(D) 89 kg
(E) 25 kg
Rationale: Total weight increased = (8 x 3) kg = 24 kg.
Weight of new person = (65 + 24) kg = 89 kg.
Answer: D
Answer: (D) 89 kg
Question: A cycle is bought for Rs.1000 and sold for Rs.1080, find the gain percent?
(A) 11
(B) 20
(C) 12
(D) 40
(E) 8
Rationale: 1000---- 80
100 ---- ? => 8%
Answer: E
Answer: (E) 8
Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. What is the length of the train?
(A) 120 metres
(B) 250 metres
(C) 324 metres
(D) 150 metres
(E) 100 meters
Rationale: Speed=60 x5/18m/sec=50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50/3	x 15m = 250 m.
ANSWER:B
Answer: (B) 250 metres
Question: A right triangle AEC has to be constructed in the xy-plane so that the right angle is at A and AE is parallel to x axis. The coordinates of A, E and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
(A) 63
(B) 336
(C) 567
(D) 3024
(E) 5040
Rationale: All the cordinates are integer hence,
possible AE values are
{-1,0}, {-1,1} ....{-1,7}: 8 ways
....
{7,-1}, {7,0} ......{7,6}: 8 ways
9*8 ways = 72
for AC values can be
{1,2}, {1,3} .... {1,7} : 6ways
......
{7,1}, {7,2} ..... {7,6} : 6 ways
7*6 = 42
Total = 72 * 42 = 3024 hence D
Answer: (D) 3024
Question: Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 6048 Nis, how much more money does Nick contribute than Archi?
(A) 128 Nis
(B) 212 Nis
(C) 234 Nis
(D) 245 Nis
(E) 288 Nis
Rationale: E:N:A 5:3:2.5
so total = 5x + 3x + 2.5 x = 10.5 x = 6048
so x = 576
Nick Contribution is 0.5 more than Archi so 0.5 x =0.5 * 576 = 288
So E. 288 Nis is the correct answer
Answer: (E) 288 Nis
Question: A furniture store owner decided to drop the price of her recliners by 20% to spur business. By the end of the week she had sold 80% more recliners. What is the percentage increase of the gross?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 44%
Rationale: Say a recliner is actually worth $100
If she sells 100 recliners then she earns $10000
After the discount of 20%, she will earn $80 per recliner and she sells 80% more ie.,180 recliners
Hence her sales tields 180*80=$14400
Increase in sales=14400-10000=$4400
So% increase = 4400*100/10000 =44%
E is the answer
Answer: (E) 44%
Question: A can do a piece of work in 2 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 12
(B) 9
(C) 8
(D) 6
(E) 3
Rationale: A's 1 hour's work = 1/2 ;
(B + C)'s 1 hour's work = 1/3 ;
(A + C)'s 1 hour's work = 1/2 .
(A + B + C)'s 1 hour's work = ( 1/2 + 1/3 ) =5/6 .
B's 1 hour's work = ( 5/6 - 1/2 ) = 1/3.
Therefore A alone will take 3 hours to do the work.
E
Answer: (E) 3
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 5 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A)  400
(B)  500
(C)  1,250
(D)  2,500
(E)  10,000
Rationale: total fish = x
percentage of second catch = (5/50)*100 = 10%
so, x * 10% = 50
x = 500 ans B.
Answer: (B)  500
Question: P is an integer divisible by 4 and Q is an integer divisible by 3. Which of the following must be odd?
(A) Q(P+1)
(B) 2P+3Q
(C) P*Q^2
(D) P^2*Q^3
(E) None of the above.
Rationale: Given: P is an integer divisible by 4 and Q is an integer divisible by 3
A. Q(P+1)
Let us take Q=6 (divisible by 3) and P=4 (divisible by 4). Q(P+1) is even.
False.
B. 2P+3Q
Let us again take Q=6 (divisible by 3) and P=4 (divisible by 4). 2P+3Q is even.
False.
C. P*Q^2
Let us again take Q=6 (divisible by 3) and P=4 (divisible by 4). P*Q^2 is even.
False.
D. P^2*Q^3
Let us again take Q=6 (divisible by 3) and P=4 (divisible by 4). P^2*Q^3 is even.
False.
E. None of the above.
E is the answer
Answer: (E) None of the above.
Question: If 12 men or 20 women can do a piece of work in 81 days, then in how many days can 9 men and 12 women together do the work?
(A) 10 days
(B) 30 days
(C) 20 days
(D) 60 days
(E) 40 days
Rationale: D
60 days
Given that 12m = 20w => 3m = 5w
9 men + 12 women = 15 women + 12 women = 27 women
20 women can do the work in 81 days. So, 27 women can do it in (20 * 81) /27 = 60 days.
Answer: (D) 60 days
Question: There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?
(A) 15
(B) 30
(C) 120
(D) 240
(E) 256
Rationale: Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence C.
Answer: (C) 120
Question: An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, …, 9 such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion when read upside down — for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise?
(A) 80
(B) 78
(C) 71
(D) 69
(E) None
Rationale: Explanation :
We need to figure out which all numbers cause a confusion when reversed : 0, 1, 6, 8, 9.
1st digit cannot be 0. So, 9 combinations are possible for the 1st digit.
2 digits are distinct. So, 2nd digit cannot be 1st digit.
Hence, again 9 combinations possible for 2nd digit. So, totally, 9 * 9 = 81 numbers are possible.
Since 1st digit is not 0, we can neglect confusions caused by 0, as, if a number with 2nd digit 0 is reversed, it will have its 1st digit as 0, and that is not possible, and hence no confusion. i.e. If we reverse 60, we get 09, but since 0 is not the 1st digit, the agency knows 09 is wrong, and hence it causes no confusion.
The remaining numbers are 1,6,8,9.
Numbers starting with 1: 16, 18, 19 cause confusion.
Numbers starting with 6: 61, 68, 69 cause confusion.
Numbers starting with 8: 81, 86, 89 cause confusion.
Numbers starting with 9: 91, 96, 98 cause confusion.
Now if you think again 69 and 96 does not cause confusion when read upside down. 69 when read upside down is 69, and 96 when read upside down is 96! So, only 10 numbers out of 81 cause confusion.
Hence, there are 71 numbers.
Answer : C
Answer: (C) 71
Question: If (x - 1)^2 = 324, which of the following could be the value of x - 4?
(A) 16
(B) 14
(C) -19
(D) -21
(E) -23
Rationale: (x - 1)^2 = 324
(x - 1) = 18 or -18
x = 19 or -17
x - 4 = 15 or -21
The answer is D.
Answer: (D) -21
Question: 300 first-time customers of a fashion store were surveyed for their shopping experience right after leaving the store. 60% of the customers in the survey had purchased clothes for less than $100. 40% of the customers in the survey reported they were overall satisfied with their purchase. 55% of the customers that had purchased clothes for less than $100 reported they were overall satisfied with their purchase. What percent of the customers surveyed purchased clothes for at least $100 and reported that they were NOT overall satisfied with their purchase?
(A) 7
(B) 25
(C) 35
(D) 45
(E) 75
Rationale: Out of 300 - 180 purchased for less than 100$120 for more
Out of 300 - 120 responded as satisfied and 180 responded disatisfied
Out of 180 ( Purchased less than 100$) - 55% = 99 responded as satisfied, So remaining Satisfied are 120 - 99 = 21
so 21 is what percentage of 300 - 7%
So the answer should be A
Answer: (A) 7
Question: Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 5 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?
(A) 2y
(B) 4y
(C) 23/5y
(D) 6y
(E) 10y
Rationale: Anthony performed for 14 days meansw Cindy performed for(14-5)=9 days.
If Cindy gives y dollars to Anthony their Daily rate will be equal.It means
(x+y)/14=(x-y)/9
Solving we get, x=23/5y
Now Anthony's Advance is x=23.5y .So answer should be C.
Answer: (C) 23/5y
Question: The product of two numbers is 2028 and their HCF is 13. What are the number of such pairs?
(A) 1
(B) 2
(C) 5
(D) 23
(E) 25
Rationale: Let the numbers be 13x and 13y ( HCF of the numbers = 13)
13x × 13y = 2028
xy = 12
co-primes with product 12 are (1, 12) and (3, 4) ( we need to take only
co-primes with product 12. If we take two numbers with product 12, but not co-prime,
the HCF will not remain as 13)
Hence the numbers with HCF 13 and product 2028
= (13 × 1, 13 × 12) and (13 × 3, 13 × 4)
= (13, 156) and (39, 52)
So, there are 2 pairs of numbers with HCF 13 and product 2028
Answer is B
Answer: (B) 2
Question: Vishal has 7 pairs of shoes; each pair is a different color. If Vishal randomly selects 2 shoes without replacement from the 14 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 2/15
(B) 1/15
(C) 1/13
(D) 1/10
(E) 1/25
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 14 shoes = 14/14 = 1
Probability of selecting the next shoe (out of 13 available) having the same color = 1/13 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/13=1/13.
C is the correct answer.
Answer: (C) 1/13
Question: Find the area of a parallelogram with base 20 cm and height 16 cm?
(A) 198 cm2
(B) 320 cm2
(C) 279 cm2
(D) 128 cm2
(E) 297 cm2
Rationale: Area of a parallelogram
= base * height
= 20 * 16 = 320 cm2
Answer:B
Answer: (B) 320 cm2
Question: five points lie on the circumference of a ellipse. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?
(A) 4
(B) 15
(C) 6
(D) 5
(E) 20
Rationale: Number of triangles can be formed out of 6 points= 5C3=10
Number of quadrilaterals can be formed out of 6 points= 5C4=5
10-5=5.
Answer=D
Answer: (D) 5
Question: How many five letter combinations can be formed using the letters of the word CARTS?
(A) 12
(B) 20
(C) 60
(D) 120
(E) 200
Rationale: The number of letters in the given word is four.
The number of five letter combinations that can be formed using these five letters is
= 5 * 4 * 3 * 2 * 1= 120.
Answer: D
Answer: (D) 120
Question: If Carol invested Rs. 2955 at 84 to obtain an income of Rs. 180, calculate the dividend from Carol's stock.
(A) 6.9
(B) 4.4
(C) 5.1
(D) 4
(E) 2
Rationale: By investing Rs.2955, income = Rs.180
By investing Rs.84, income = 180Ã—84/2955=5.1
ie, dividend = 5.1%
Answer is C.
Answer: (C) 5.1
Question: Jar X is 1/5 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity?
(A) 2/5
(B) 3/5
(C) 7/10
(D) 7/20
(E) 9/20
Rationale: Let P be the capacity of Jar X.
The amount of water in Jar Y is 1/2*P/2=P/4
Then the total amount in Jar X is P/5+P/4=9/20
The answer is E.
Answer: (E) 9/20
Question: If Rs. 64 amount to Rs. 83.20 in 2 years, what will Rs. 86 amount to in 4 years at the same rate percent per annum ?
(A) Rs. 114.80
(B) Rs. 86.70
(C) Rs. 55.40
(D) Rs. 51.60
(E) None
Rationale: Solution
P = Rs. 64,S.I. = Rs. (83.20 - 64) = Rs. 19.20, T= 2 years.
So, rate = (100x19.20/64x2)= 15%.
Now, P = Rs. 86, R = 15% ,T = 4 years.
∴ S.I. = Rs.(86x15x4/100) Rs. 51.60.
Answer D
Answer: (D) Rs. 51.60
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 276 m
(B) 167 m
(C) 245 metres
(D) 167 m
(E) 178 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer:C
Answer: (C) 245 metres
Question: Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 8, 9, 10, 11, 12, 13
II. 12, 12, 12, 12, 12, 12
III. 47, 56, 58, 60, 64, 69
(A) I, II, III
(B) II, I, III
(C) III, I, II
(D) II, III, I
(E) III, II, I
Rationale: out of three given sets,
II has all numbers same, so it has zero standard deviation hence it is Least
I has consecutive numbers , hence all are closedly spaced hence std deviation will be less
while in III,numbers are spread widely hence std deviation should be more than III
hence order should be II, I,III
IMO B
Answer: (B) II, I, III
Question: Find the number of shares that can be bought for Rs.8200 if the market value is Rs.20 each with brokerage being 3.2%.
(A) 237
(B) 270
(C) 177
(D) 166
(E) 397.2
Rationale: Explanation:
Cost of each share = (20 + 3.2% of 20) = Rs.20.64
Therefore, number of shares = 8200/20.64 = 397.2
ANSWER:E
Answer: (E) 397.2
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
(A) 21:32
(B) 32:21
(C) 12:17
(D) 17:12
(E) 15:11
Rationale: Explanation:
Here capital is not the same.
Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio
=(20000Ã—6+15000Ã—6)=(20000Ã—6+15000Ã—6)
Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio
=(30000Ã—4+50000Ã—4)=(30000Ã—4+50000Ã—4)
Suresh : Kiran
=(20000Ã—6+15000Ã—6)=(20000Ã—6+15000Ã—6) :(30000Ã—4+50000Ã—4):(30000Ã—4+50000Ã—4)
=(20Ã—6+15Ã—6):(30Ã—4+50Ã—4)=(20Ã—3+15Ã—3):(30Ã—2:50Ã—2)=105:160=21:32
ANSWER IS A
Answer: (A) 21:32
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 276 games will be played during the tournament. Find the number of participants.
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: Let P be the number of participants.
PC2 = 276
(P)(P-1) = 552 = 24*23
P = 24
The answer is C.
Answer: (C) 24
Question: The overall age of X and Y is 19 year greater than the overall age of Y and Z. Z is how many decades younger that X?
(A) 11
(B) 15
(C) 12
(D) 19
(E) 20
Rationale: D
19
(X + Y) â€“ (Y + Z) = 19
X â€“ Z = 19
Answer: (D) 19
Question: When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country?
(A) 166 2/7
(B) 166 2/3
(C) 166 2/9
(D) 166 2/3
(E) 166 2/2
Rationale: 5% - 2% = 3%
3% ---- 5
100% ---- ? => 166 2/3
Answer: D
Answer: (D) 166 2/3
Question: A bag of potatoes weighs 36 lbs divided by half of its weight. How much does the bag of potatoes weight?
(A) 20 lb
(B) 30 lb
(C) 10 lb
(D) 15 lb
(E) 36 lb
Rationale: Sol.
36÷3 = 12.
Answer : E
Answer: (E) 36 lb
Question: Last year, Company Z made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his two other partners. In terms of q, how much did each of the other partners receive?
(A) q/4
(B) q/5
(C) q/6
(D) q/7
(E) q/8
Rationale: Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 2
Profit to each partner = (q/2)/2 = q/4
Answer: A
Answer: (A) q/4
Question: The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 120 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 70, 10 kmph
(B) 35, 27 kmph
(C) 110, 10 kmph
(D) 45, 55 kmph
(E) 45, 65 kmph
Rationale: Speed of the boat in still water = (100+120)/2 = 110 kmph. Speed of the stream = (120-100)/2 = 10 kmph
ANSWER:C
Answer: (C) 110, 10 kmph
Question: In a workshop there are 2 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
(A) 168.
(B) 80.
(C) 56.
(D) 40.
(E) 16.
Rationale: ways to select one shelf = 2
ways to select one bed = 2
ways to select one of the following: a chair or a closet = 7+3 = 10
ways to select all of them together = 2*2*10 = 40
Hence, D is the answer.
Answer: (D) 40.
Question: When positive integer x is divided by positive integer y, the remainder is 12. If x/y = 75.12, what is the value of y?
(A) 84
(B) 98
(C) 51
(D) 65
(E) 100
Rationale: When positive integer x is divided by positive integer y, the remainder is 12 --> x=qy+12;
x/y=75.12 --> x=75y+0.12y (so q above equals to 75);
0.12y=12 --> y=100.
Answer: E.
Answer: (E) 100
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 1 less, he would have made a profit of 10%. The C.P. of the article was
(A) Rs 100
(B) Rs 150
(C) Rs 200
(D) Rs 250
(E) None of these
Rationale: Explanation:
Let original Cost price is x
Its Selling price = 105/100 * x = 21x/20
New Cost price = 95/100 * x = 19x/20
New Selling price = 110/100 * 19x/20 = 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 200
Option C
Answer: (C) Rs 200
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 88 players took part in that tournament. How many matches were played?
(A) 90 matches
(B) 95 matches
(C) 99 matches
(D) 85 matches
(E) 87 matches
Rationale: E 87 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 87 matches were played.
Answer: (E) 87 matches