mathewhe/aqua_rat huggingface dataset:
Question: Set A: 3, w, 8, 10
Set B: 4, y, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – w?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: So we have even no. of elements in the Set
So median is the average of Middle two numbers
(w+8)/2= (y+9)/2
y - w= -1
Answer B
Answer: (B) -1
Question: The curved surface of a sphere is 64 π cm2. Find its radius?
(A) 8
(B) 6
(C) 4
(D) 2
(E) 5
Rationale: 4 πr2
= 64
=> r = 4
Answer: C
Answer: (C) 4
Question: H is a positive integer and 225 and 216 are both divisors of H. If H=(2^a)*(3^b)*(5^c), where a, b and c are positive integers, what is the least possible value of a+ b+ c?
(A) 4
(B) 8
(C) 6
(D) 7
(E) 5
Rationale: Lets make factorization of 225 and 216 ..
225 = 5 X 5 X 3 X 3 X 3
216 = 2 X 2 X 2 X 3 X 3 X 3
H would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2 = 8(B) (answer) ...
Answer: (B) 8
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 36 years now, the son's age five years back was
(A) 13years
(B) 15years
(C) 17years
(D) 19years
(E) 20years
Rationale: Let the son's present age be x years. Then, (36 - x) = x
2x = 36.
x = 18.
Son's age 5 years back (18 - 5) = 13 years.
A)
Answer: (A) 13years
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 18kmph and the other is going towards south 20kmph. What time will they take to be 114 km apart?
(A) 1 1/4 hours
(B) 3 hours
(C) 4hours
(D) 3 3/4 hours
(E) 6hours
Rationale: To be (18+20) km apart, they take 1 hour
To be 114 km apart, they take 1/38 * 114 = 3 hrs
Answer is B
Answer: (B) 3 hours
Question: A certain list of 301 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?
(A)  75 and 80
(B)  75 and 75
(C)  70 and 75
(D)  74 and 75
(E)  70 and 80
Rationale: Deviation means spreading of the numbers from one median point value..
as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.
so 75 and 75 are the most close numbers and they will increase the number of elements in the set without changing the median value.
B
Answer: (B)  75 and 75
Question: Find the one which does not belong to that group ?
(A) 30
(B) 82
(C) 27
(D) 62
(E) 11
Rationale: Explanation:
27, 36, 72 and 45 are divisible by 9, but not 30.
Answer: A
Answer: (A) 30
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) m
(B) m
(C) m
(D) m
(E) of these
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
ANSWER:B
Answer: (B) m
Question: A train 450 m long running at 126 kmph crosses a platform in 20 sec. What is the length of the platform?
(A) 271
(B) 250
(C) 350
(D) 277
(E) 232
Rationale: Length of the platform = 126 * 5/18 * 20 = 700 – 450
= 250
Answer:B
Answer: (B) 250
Question: An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?
(A) 12.50 %
(B) 13.50 %
(C) 14 %
(D) 14.50 %
(E) None
Rationale: Sol.
Let C.P. = Rs. 100. Then, marked price = Rs. 150.
S.P. = 75% of Rs. 150 = Rs. 112.50.
∴ Gain% = 12.50%.
Answer A
Answer: (A) 12.50 %
Question: I bought two books; for Rs.600. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 197
(B) 280
(C) 189
(D) 278
(E) 350
Rationale: x*(85/100)
= (600 - x)119/100
x = 350
Answer: E
Answer: (E) 350
Question: If the growth in production of company A from 1994 to 1995 was 25% and that from 1995 to 1996 was 60%, then what percentage growth took place from 1994 to 1996?
(A) 85%
(B) 75%
(C) 200%
(D) 100%
(E) None of these
Rationale: Percentage growth from 1994 to 1996
= +25 + 60 + 25×60/100= +100%
Answer D
Answer: (D) 100%
Question: Jack bought 150 packets of chocolate. He was able to sell 1/3 of them at a 20% profit, another 1/3 of them at zero profit and the remainder was sold at a 10% loss. Find the total profit or loss made by the person after selling those 150 packets. A packet sold at a loss had a price of $9.
Please provide an intuitive answer if possible. Thanks!!
(A) Profit of $50
(B) Profit of $20
(C) Loss of $25
(D) Profit of $30
(E) Loss of $35
Rationale: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.
50 packets was sold at a 20% profit --> gives profit of 10*0.2*50 = $100.
50 packets was sold at a 10% loss --> gives loss of 10*0.1*50 = $50.
The overall Profit is $100 - $50 = $50.
Answer: A.
Answer: (A) Profit of $50
Question: A sum of money is borrowed and paid back in two annual installments of Rs. 882 each allowing 5% C.I. The sum borrowed was?
(A) 1647
(B) 1640
(C) 2888
(D) 2298
(E) 2709
Rationale: Principal = (P.W. of Rs. 882 due 1 year hence) + (P.W. of Rs. 882 due 2 years hence)
= [882/(1 + 5/100) + 882/(1 + 5/100)2]
= (882 * 20)/21 + (882 * 400)/441 = Rs. 1640.Answer: B
Answer: (B) 1640
Question: Six pipes are fitted to a water tank. Some of these are inlet pipes and the others outlet pipes. Each inlet pipe can fill the tank in 9 hours and each outlet pipe can empty the tank in 6 hours. On opening all the pipes, an empty tank is filled in 9 hours. How many inlet pipes are there?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 6
Rationale: x / 9 – y / 6 = 1/9; 2x – 3y + 2
We can compute that x = 4 and y = 2.
Thus, Inlet pipe = x = 4.
Answer: B
Answer: (B) 4
Question: There are 9 executives, including the CEO and CFO, that are asked to form a small team of 5 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?
(A) 85
(B) 87
(C) 89
(D) 91
(E) 93
Rationale: The total number of ways to form a team of 5 is 9C5=126.
We need to subtract the number of teams that have both the CEO and the CFO.
The number of teams with both the CEO and CFO is 7C3=35.
The number of ways to form an acceptable team is 126-35=91.
The answer is D.
Answer: (D) 91
Question: The Guests at a football banquet consumed a total of 337 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
(A) 160
(B) 161
(C) 162
(D) 163
(E) 169
Rationale: To minimize one quantity maximize other.
168*2 (max possible amount of food a guest could consume) = 336 pounds, so there must be more than 168 guests, next integer is 169.
Answer: E.
Answer: (E) 169
Question: The grade point average of the entire class is 87. If the average of one third of the class is 95, what is the average of the rest of the class?
(A) 81
(B) 82
(C) 83
(D) 84
(E) 85
Rationale: Let x be the number of students in the class.
Let P be the average of the rest of the class.
87x = (1/3)95x + (2/3)(P)x
261 = 95 + 2P
2P = 166
P = 83.
The answer is C.
Answer: (C) 83
Question: The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?
(A) 25
(B) 35
(C) 38
(D) 29
(E) 22
Rationale: excluded number = (27 x 5) - (25 x 4)
= 135 - 100
= 35.
Answer: B
Answer: (B) 35
Question: Find the odd man out
1, 2, 5, 14, 41, 120
(A) 2
(B) 14
(C) 124
(D) 120
(E) 21
Rationale: 1*3-1 =2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3 -1 = 122
ANSWER:D
Answer: (D) 120
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 68
(D) 88
(E) 78
Rationale: We have: l = 20 ft and lb = 680 sq. ft.
So, b = 34 ft.
Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.
ANSWER:D
Answer: (D) 88
Question: In a class,7 students like to play Basketball and 5 like to play Cricket. 3 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
(A) 12
(B) 15
(C) 16
(D) 9
(E) 22
Rationale: Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
7 +5 - 3 = 9
D)
Answer: (D) 9
Question: If a quarter kg of onions costs 60 paise, how many paise will 100 gm cost?
(A) 24 paise
(B) 65 paise
(C) 56 paise
(D) 87 paise
(E) 15 paise
Rationale: Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 60 : x
250 * x = (100 * 60)
x = (100 * 60) / 250
x = 24
ANSWER: A
Answer: (A) 24 paise
Question: In assembling a Bluetooth device, a factory uses one of two kinds of modules. One module costs $10 and the other one, that is cheaper, costs $6. The factory holds a $80 worth stock of 12 modules. How many of the modules in the stock are of the cheaper kind?
(A) 20
(B) 25
(C) 10
(D) 30
(E) 35
Rationale: So the number of $6 modules must be 10 so that the leftover 2 modules are of $10 which will give a total value $80. 10*6+2*10 = 60+20=80
Answer : C
Answer: (C) 10
Question: If x/y = 9/8, Then (8x + 7y) / (8x â€“ 7y) = ?
(A) 8
(B) 7
(C) 10
(D) 9
(E) 6
Rationale: Answer
Dividing numerator as well as denominator by y, we get
Given Exp. = (8x + 7y) / (8x â€“ 7y) = (8x/y + 7) / (8x/y â€“ 7)
Since x/y = 9/8
this implies that
=[(8*9)/8 +7]/[(8*9)/8 -7)]
= (9+ 7) / (9 - 7)
= 8
Option: A
Answer: (A) 8
Question: There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
(A) 1023
(B) 6000
(C) 1980
(D) 1800
(E) 1450
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
ANSWER D 1800
Answer: (D) 1800
Question: If 10 crates have 94 apples each and how many apples more is required in order to make 100 apples in each crate?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 60
Rationale: Each crate requires 6 apples and totally there are 10 crates so required apples = 10 * 6 = 60
Answer: E
Answer: (E) 60
Question: How many integers between 314,700 and 458,600 have tens digit 1 and units digit 3?
(A) 10,300
(B) 10,030
(C) 1,353
(D) 1,352
(E) 1,439
Rationale: There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ...
The difference between 314,700 and 458,600 is 458,600-314,700=143,900 - one number per each hundred gives 143,900/100=1,439 numbers.
Answer: E.
Answer: (E) 1,439
Question: A patient was given four pills which he is required to take one after every thirty-five minutes.
How long can the pills run for him?
(A) 1 hour and 30 minutes
(B) 1 hour and 20 minutes
(C) 1 hour and 45 minutes
(D) 1 hour and 15 minutes
(E) 1 hour and 42 minutes
Rationale: He took the first pill at the zero minute.
He took the second pill after 20 minutes = 0+35=35
He took the third pill after 20 minutes = 35+35=70
He took the fourth pill after 20 minutes = 70+35=105
Then it will last for 105 minutes or an hour and 45 minutes.
Answer C
Answer: (C) 1 hour and 45 minutes
Question: In a kilometer race, A beats B by 80 meters or 8 seconds. What time does A take to complete the race?
(A) 77 sec
(B) 92 sec
(C) 67 sec
(D) 16 sec
(E) 76 sec
Rationale: Time taken by B run 1000 meters = (1000 * 8)/80 = 100 sec.
Time taken by A = 100 - 8 = 92 sec.Answer: B
Answer: (B) 92 sec
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 62.9
(C) 52.1
(D) 62.6
(E) 62.1
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Answer: (A) 62.5
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
(A) Difference is 3
(B) Difference is 4
(C) Difference is 9
(D) Cannot be determined
(E) None of these
Rationale: EXPLANATION
Let the ten’s digit be x and unit’s digit be y.
Then, (10x + y) – (10y + x) = 36
9(x – y) = 36
x – y = 4.
Answer B
Answer: (B) Difference is 4
Question: The sum of two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is
(A) 10
(B) 11
(C) 12
(D) 16
(E) 17
Rationale: Solution
Let the number be x and (22-x)
‹=› 11x = 132
‹=›x = 12
So,the numbers are 12&10.
Answer C
Answer: (C) 12
Question: Jackson invested $500,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?
(A) $115,384
(B) $120,000
(C) $121,072
(D) $124,129
(E) $130,000
Rationale: x be the amount invested in account P
0.12*x +(500000-x)*0.25=60,000
15000/.13=x
x=1500000/13=11...=$121,072
hence answer is C
Answer: (C) $121,072
Question: Find the principle on a certain sum of money at 5% per annum for 5 years if the amount being Rs.1120?
(A) 896
(B) 1067
(C) 1977
(D) 1056
(E) 1097
Rationale: 1120 = P [1 + (5*5)/100]
P= 896
Answer: A
Answer: (A) 896
Question: An engagement team consists of a project manager, team leader, and four consultants. There are 5 candidates for the position of project manager, 8 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?
(A) 850
(B) 900
(C) 980
(D) 1000
(E) 1200
Rationale: Answer= Total number combinations - Total number of combinations with constraints
Total number of combinations = 5C1*8C1*7C4= 1400
Total number of combinations with constraints = 5C1*8C1*5C2=400
Answer=1400-400=1000
ANSWER: D
Answer: (D) 1000
Question: From a group of 3 signers and 3 comedians, a show organizer might select two singers and two comedians to appear one after another in the show, how many different ways an organizer can arrange the performers in the show.
(A) 221
(B) 216
(C) 312
(D) 62
(E) 124
Rationale: Ways to select 2 Singers out of 3 = 3C2 = 3
Ways to select 2 Comedians out of 3 = 3C2 = 3
Ways to rearrange 4 performers = !4 = 24
Total combinations = 3*3*24=216.
ANS:B
Answer: (B) 216
Question: How many different arrangements of A, B, C, D, and E are possible where B and D is not adjacent to E?
(A) 96
(B) 72
(C) 32
(D) 30
(E) 1
Rationale: So you have A,B,C,D,E
five possible ways to arrange it = 5! = 120
A,B,C,(DE) = 4! = 24 x 2 = 48
120 -48 =72 possible ways
B
Answer: (B) 72
Question: The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
(A) 178.27 cm
(B) 178.29 cm
(C) 978.29 cm
(D) 178.89 cm
(E) 176.29 cm
Rationale: Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm
= 180 * 35 cm - 166 cm + 106 cm/35 = 180 cm - 60 /35 cm
= 180 cm - 1.71 cm = 178.29 cm.
Answer: B
Answer: (B) 178.29 cm
Question: An error 3% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
(A) 6.05
(B) 6.09
(C) 6.03
(D) 6.02
(E) 6.01
Rationale: Explanation:
100 cm is read as 103 cm.
A1 =(100 × 100)cm2 = 10000
and A2= (103 × 103)cm2= 10609
(A2 - A1) = 10609-10000 = 609
=> 609/10000*100 =6.09
Answer : B
Answer: (B) 6.09
Question: The probability of a team winning a match given Matt is playing the match is 0.70. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.9.
If it is known that the team has won the last match, what is the probability that Matt played the match?
(A) A)0.8321
(B) B)0.7
(C) C)0.8571
(D) D)0.926
(E) E)0.896
Rationale: Out of 100 matches:
Matt is plays in 90 and not plays in 10.
Out of 90 matches Matt plays in, team wins 0.70*90 = 63.
Out of 10 matches Matt does not play in, team wins 0.5*10 = 5.
So, out of 100 matches 63 + 5 = 68 are won.
It is known that the team has won the last match. Out of 68 matches won, Matt is in 63: 63/68 = 0.926...
Answer: D.
Answer: (D) D)0.926
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
(A) 22
(B) 73
(C) 99
(D) 42
(E) 11
Rationale: Explanation:
Just go in reverse order.
Check the options with th subtracting 18 from each option for getting reverse number.
42 – 18 = 24 (which is in reverse).
So answer is 42.
Answer D
Answer: (D) 42
Question: An equilateral triangle of sides 3 inch each is given. How many equilateral triangles of side 1 inch can be formed from it?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: volume of equilateral triangle = 1/2*bh (b base, h height)
volume of 3 inch Eq tri =1/2*3*20598 = 1/2*1*.866*N(volume of 1 inch eq tri and N is no of 1 inch triangles9
so ans is 9 ANSWER:B
Answer: (B) 9
Question: While working alone at their respective constant rates, server P uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files?
(A)  2 hr
(B)  2hr 20 min
(C)  2hr 40 min
(D)  5 hr 40 min
(E)  6hr
Rationale: Server P processes 480/4 files per hour = 120 per hour
Server Y processes 180/8 files per hour = 60 per hour
Total files processed per hour when P and Y work together = 120+60 per hour = 180 files per hour
480/180 = 2 2/3 hours=C
Answer: (C)  2hr 40 min
Question: In a flower shop there were 10 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is
(A) 12
(B) 20
(C) 18
(D) 19
(E) None of these
Rationale: Answer
Now required average
= old average x Multiplicand
= 10 x 2 = 20
Correct Option: B
Answer: (B) 20
Question: In certain year in Country C, x sets of twins and y sets of triplets were born. If there were z total babies born in Country C in this year, and x and y were both greater than 0, which of the following represents the fraction W of all babies born who were NOT part of a set of twins or triplets?
(A) z - 2x - 3y
(B) (2x+3y)/z
(C) (x+y)/z
(D) 1 - (2x+3y)/z
(E) 1 - (x+y)/z
Rationale: X set of twins implies 2x babies of twin category.
Y set of triplets means 3y babies of triplet category.
Let K be the babies other than twin or triplet category.
Total babies = z = 2x+3y+k.
or K=Z-(2x+3y)
=> Fraction of babies other than twin or triplet categories = K/Z = Z-(2x+3y)/Z.
W= 1- (2x+3y)/Z. Hence answer is D.
Answer: (D) 1 - (2x+3y)/z
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years?
(A) 306.78
(B) 306.79
(C) 306.04
(D) 306.18
(E) 306.19
Rationale: A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer: C
Answer: (C) 306.04
Question: A sum of $500 amounts to 600 in 2 years at simple interest. If the interest rate is increased by 10% it would amount to how much ?
(A) $500
(B) $700
(C) $800
(D) $600
(E) $300
Rationale: S.I = 600-500 = 100
P = $500
T = 2 years
R = 100*100 / 500*2 = 10%
New rate = 10+10 =20%
New S.I. = 500*20*2/100 = $200
New amount = 500+200 = $700
Answer is B
Answer: (B) $700
Question: Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.870?
(A) Rs.700
(B) Rs.780
(C) Rs.750
(D) Rs.1000
(E) None of these
Rationale: Explanation:
870 = P [1 + (5*16/5)/100]
P= 750
Answer: Option C
Answer: (C) Rs.750
Question: 0.35 represents what percent of 0.007?
(A) 0.05%
(B) 0.5%
(C) 5%
(D) 500%
(E) 5000%
Rationale: One more method
0.35 represents what percent of 0.007?
Adjusting the decimal
350 represents what percent of 7?
Divide by 7
50 represents what percent of 1?
Answer = 50*100 = 5000%
ANSWER:E
Answer: (E) 5000%
Question: At a meeting, 7 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 12
(B) 72
(C) 120
(D) 144
(E) 720
Rationale: The number of arrangements of n distinct objects in a row is given by n!
The number of arrangements of n distinct objects in a circle is given by (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:
R=n!-n=(n−1)!
(n−1)!=(7−1)!=720
Answer: E
Answer: (E) 720
Question: The least among the following is:
(A) 0.2
(B) 1 ÷ 0.2
(C) 0.2 (power 2)
(D) 22/7
(E) 1
Rationale: 1 ÷ 0.2 = 1/0.2 =10/2= 5;
22/7 = 3.14;
(0.2)(power 2) = 0.04;
0.04 < 1 < 3.14 <5.
Since 0.04 is the least, so (0.2)2 is the least.
Answer is C.
Answer: (C) 0.2 (power 2)
Question: A boat running downstream covers a distance of 24 km in 3 hours while for covering the same distance upstream,it takes 4 hours.What is the speed of the boat in still water ?
(A) 4 km/hr
(B) 6 km/hr
(C) 8 km/hr
(D) 7 km/hr
(E) None of these
Rationale: Solution
Rate downstream =(24/3) kmph = 8 kmph, Rate upstream =(24/4) = 6 kmph.
∴ Speed in still water =1/2(8+6) kmph = 7 kmph.
Answer D
Answer: (D) 7 km/hr
Question: In a Olympic a country get total 222 medals. If the ratio of gold silver and bronze medals is 5:17:15. find the number of gold medals?
(A) 16
(B) 25
(C) 32
(D) 15
(E) 30
Rationale: Let the number of gold silver and bronze medal are 5x, 17x, and 15x
5x+17x+15x = 222
37x = 222
x = 6
number of gold medals = 6*5 = 30
Answer : E
Answer: (E) 30
Question: Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 9 from the product of their ages a year from today. What is their age today?
(A) 2.
(B) 4.
(C) 5.
(D) 7
(E) 9.
Rationale: ad = (a+1) (d+1) -9
0= a+d-8
a+d = 8
a=d (as they are twin brothers)
a=d=4
B is the answer
Answer: (B) 4.
Question: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number F of people surveyed by the company?
(A) 46
(B) 80
(C) F=90
(D) F=100
(E) 200
Rationale: 100 = x + x - 20 + 23 - 23
x = 60,
So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%
23% of the total no. of people should be an integer. So, A,BC are out.
60% of D and 40% of D are both integers. So, D satisfies all conditions.
So, answer is D.
Answer: (D) F=100
Question: The product of all prime numbers less than or equal to nine are?
(A) 210
(B) 125
(C) 15
(D) 55
(E) 100
Rationale: A)
Answer: (A) 210
Question: 7386038 is divisible by
(A) 3
(B) 4
(C) 9
(D) 11
(E) 13
Rationale: Explanation:
The given number is 7386038.
The sum of the digits at even places is = 3+ 6+ 3=12.
The sum of the digits at odd places is = 7+ 8+ 0+ 8 = 23.
The difference is given by 23-12 = 11
Answer: D
Answer: (D) 11