mathewhe/aqua_rat huggingface dataset:
Question: A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 200 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 89
(B) 20
(C) 40
(D) 88
(E) 34
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 200 + 200 = 360 m.
Time taken = 400/10 = 40 sec.
Answer: Option C
Answer: (C) 40
Question: The ‘moving walkway’ is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate R of movement for his trip along the moving walkway?
(A) 2 feet per second
(B) 2.5 feet per second
(C) 3 feet per second
(D) 4 feet per second
(E) 5 feet per second
Rationale: A, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average R MUST bebetween3-6 ft per second or the Earth is FLAT!!!.
So we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft per second before he stopped walking. That leaves only answer E as plausible.
Answer: (E) 5 feet per second
Question: If x is a positive integer, which of the following could NOT be the square of x?
(A) 5,008,644
(B) 5,004,169
(C) 4,999,696
(D) 4,995,225
(E) 4,990,752
Rationale: A perfect square will never end in 2, 3, 7 or 8. (last digit cannot be 2, 3, 7 or 8)
Here E is the odd one out.
Answer: E
Answer: (E) 4,990,752
Question: The product of two successive numbers is 4556. Which of the following is the larger of the two numbers?
(A) 68
(B) 67
(C) 78
(D) 87
(E) 66
Rationale: Let the two successive numbers be n, n + 1.
It is given that n(n + 1) = 4556.
=> n2 + n - 4556 = 0
=> n2 + 68n - 67n - 4556 = 0
=> n(n + 68) - 67(n + 68) = 0
=> n = 67 and (n + 1) = 68.
ANSWER:A
Answer: (A) 68
Question: If x^2 + 1/x^2 = 2,what is the value of x^4 + 1/x^4 ?
(A) 10
(B) 2
(C) 4
(D) 16
(E) 18
Rationale: IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 2 andSQUAREboth sides:
(x² + 1/x²)²= 4
So, (x² + 1/x²)(x² + 1/x²) = 4
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 4
Simplify: x⁴ + 1/x⁴ = 2
Answer: B
Answer: (B) 2
Question: If (5)(x^2) has three different prime factors, at most how many different prime factors does x have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x can have at most 3 prime factors, namely the prime factor 5 plus two others.
If x had more than this number of prime factors, then (5)(x^2) would have more than 3 prime factors.
The answer is C.
Answer: (C) 3
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many even five-digit numbers are palindromes?
(A) 40
(B) 400
(C) 500
(D) 5,000
(E) 100,000
Rationale: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144.
The middle number in the five-digit could be 0-9 ( 10 ways), e.g 22522, 22822
The 2nd and fourth numbers could must also be same i.e 0-9( 10 ways) e.g 23432, 85658
we thus have, 4 *10*10 = 400.
answer is B ( 400)
Answer: (B) 400
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 1/2 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
(A) 1/2
(B) 2/5
(C) 8/11
(D) 4/5
(E) 5/8
Rationale: Method: X = No. of boxes loaded by day crew.
Boxes by night crew = 3/4 * 1/2 X = 3/8 X
% loaded by day crew = X/(X + 3/8X) = 8/11
Answer C
Answer: (C) 8/11
Question: If 7/6 of a pencil is purple, 4/3 of the remaining is black and the remaining 1/2 is blue, what is the total length of the pencil?
(A) 5
(B) 3
(C) 1
(D) 4
(E) 2
Rationale: Purple is 7/6 Black is 4/3 which can also be written as 8/6Blue is 1/2 which can also be written as 3/67/6 + 8/6 + 3/16= 3Answer is B) 3
Answer: (B) 3
Question: Given 2 integers a and b, if a is negative and b is positive, which of the following options must be positive?
(A) ab
(B) a/b
(C) 4a/b
(D) (a + b)^4
(E) 2ab
Rationale: A.ab
-ve*+ve= -ve
will be negative
B. a/b
-ve/+ve=-ve
will be negative
C. 4a/b
-ve/+ve=-ve
D. (a + b)^4
= (a + b)^4 will be positive irrespective of the absolute values of x and y
will be positive always
E. 2ab
-ve*+ve= -ve
will be negative
Answer D
Answer: (D) (a + b)^4
Question: Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 + S3 + S2 – S1. What is the value of K?
(A) 67
(B) 50
(C) 45
(D) 272
(E) 36
Rationale: I used brute force for this question:
S6: 36+30+94=160
S5: 25+25+94=144
S4: 16+20+94=130
S3: 9+15+94=118
S2: 4+10+94=108
S1: 1+5+94=100
S6-S5+S4+S3+S2-S1= 16+248+8=272
Answer D
Answer: (D) 272
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
(A) 34
(B) 37
(C) 46
(D) 54
(E) 58
Rationale: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
C
Answer: (C) 46
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 15%, then the cost price of the article is:
(A) 500
(B) 334
(C) 555
(D) 536
(E) 5598
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/115 = Rs. 536
Answer: Option D
Answer: (D) 536
Question: A bag is filled with pennies and nickels in the ratio of 5 to 3. There are 30 nickles in the bag, how many coins are there in that bag?
(A) 40
(B) 50
(C) 65
(D) 70
(E) 80
Rationale: A ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form
number of pennies = 5x and number of nickels = 3x
But we know the number of nickels, 30. Hence
3x = 30
Solve for x
x = 10
The total number of coins is given by
5x + 3x = 8x = 8 × 10 = 80
E
Answer: (E) 80
Question: James just found out that has to work a 12 hour shift on Christmas Day, from 3pm until 3am. Since that day is a national holiday, he will get paid 2 times his normal hourly rate for the entire shift. Additionally, the state he lives in has a law that requires an overtime rate, equal to 1.5 times the shift's hourly rate, for every hour over 8 hours in one day. Finally, he will get paid a "night premium" of 20% above the shift's hourly rate for any time worked after 10pm. James' regular rate is $16 per hour. Assuming he works his full shift as scheduled, how much money will James make (before taxes) on Christmas day?
(A) $460.40
(B) $576.00
(C) $432.00
(D) $492.80
(E) $518.40
Rationale: Holiday Rate calculation: Regular Hourly rate of $16 x 2 = $32 per hour
Overtime Rate calculation: Holiday shift rate $32 x 1.5 = $48 per hour
Night premium: Before 8th hour, Holiday rate $32 + 20%, calculation would be 32 x .20 = 6.4, adding 6.4 to 32 = $38.40 per hour
Night premium: After 8th hour, Holiday overtime rate $48 + 20%, calculation would be 48 x .20 = 9.6, adding 9.6 to 48 = $57.60 per hour
SHIFT HOURS BREAKDOWN:
3pm-10pm = 7 hours @ Holiday rate $32
10pm-11pm = 1 hour @ Holiday rate w/ night premium $38.40
11pm-3am = 4 hours @ Holiday Overtime rate w/ night premium $57.60
$32 x 7 = $224
$38.40 x 1 = $38.40
$57.60 x 4 = $230.40
Total for entire 12-hour shift, pre-taxes: $492.80
Answer: (D) $492.80
Question: Shop Offered 25% offer for every Shirt, Smith bought a shirt at Rs. 560. and What was the shop's original selling Price?
(A) 500
(B) 550
(C) 746
(D) 700
(E) 750
Rationale: SP* (75/100) = 560
SP= 7.46 * 100 => CP = 746
Answer:C
Answer: (C) 746
Question: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.05, what is value of J?
(A) 22
(B) 56
(C) 280
(D) 112
(E) 175
Rationale: 1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.08, the decimal part of the decimal quotient, must equal the remainder, 14, divided by the divisor J.
0.05 = 14/J
0.05*J = 14
J = 14/0.05 = 1400/5 = 280
So J = 280, answer = C.
Answer: (C) 280
Question: A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts four hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
(A) 3
(B) 4.5
(C) 8
(D) d) 5.5
(E) e) 5
Rationale: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.
We know their rates are 30, 40 and 60.
Say the time taken by B is T hrs. Then A takes 4+T hrs. And we need to find the time taken by K.
Distance covered by A = Distance covered by B
30*(4+T) = 40*T
T = 12 hrs
Distance covered by B = Distance covered by K
40*T = 60*Time taken by K
Time taken by K = 40*12/60 = 8 hrs
Time taken by A = 4+T = 4+12 = 16 hrs
Time taken by K = 8 hrs
So K starts 16-8 = 8 hrs after A. (answer C)
Answer: (C) 8
Question: Find the compound interest and the amount on Rs.3000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) s.261.88
(B) s.440.88
(C) s.472.88
(D) s.346.88
(E) s.446.88
Rationale: A = 3000(21/20)3
= 3472.88
= 3000
---------
472.88
ANSWER:C
Answer: (C) s.472.88
Question: How many three-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.
(A) 85
(B) 90
(C) 95
(D) 100
(E) 105
Rationale: N=(4*5-1)*5*=85
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 44 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
A
Answer: (A) 85
Question: A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length W of the fence including the fence posts on each end?
(A) mn
(B) m(n + x)
(C) W=m(n + x) + x
(D) m(n + x) + 2x
(E) 2mn
Rationale: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.
The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.
Answer: C.
Answer: (C) W=m(n + x) + x
Question: If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/25, then the reciprocal of n must be
(A) Less than -5
(B) Between -1 and -1/5
(C) Between -1/5 and 0
(D) Between 0 and 1/5
(E) Greater than 5
Rationale: n^2 < 1/25
abs(n) < 1/5
Since n<0, then 0 > n > -1/5
1/n < -5
The answer is A.
Answer: (A) Less than -5
Question: A rainstorm increased the amount of water stored in State J reservoirs from 130 billion gallons to 160 billion gallons. If the storm increased the amount of water in the reservoirs to 80 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 75
(B) 70
(C) 65
(D) 85
(E) 90
Rationale: Let total capacity be x
we know 160 = 0.80x
x = 160/0.80 = 200
Prior to storm, we had 130 bn gallons
200-130 = 70
Answer : B
Answer: (B) 70
Question: In a office work is distribute between p persons. If 1/7 members are absent then work increased for each person is?
(A) 13.67%
(B) 14.67%
(C) 15.67%
(D) 16.67%
(E) 17.67%
Rationale: let total % of work is 100%
total person=p
1/7 person are absent of total person . so absent person is 1/7p ie p/7.
left person is, p-p/7=6p/7.
p person do the work 100%
1 person do the work 100*p%
6p/7 person do the work (100*p*7)/6p%=116.67%
work increased for each person is=(116.67-100)%=16.67%
ANSWER:D
Answer: (D) 16.67%
Question: Two persons start running simultaneously around a circular track of length 500 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 11
(B) 10
(C) 28
(D) 45
(E) 12
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 500 / (15 + 25)5/18 = 500* 18 / 40 * 5 = 45 seconds.
Answer: D
Answer: (D) 45
Question: A certain telescope increases the visual range at a particular location from 80 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?
(A)  30%
(B)  33 1/2%
(C)  40%
(D)  60%
(E)  87.5%
Rationale: Original visual range = 80 km
New visual range = 150 km
Percent increase in the visual range by using the telescope
= (150-80)/80 * 100%
= 7/8 * 100%
= 87.5 %
Answer E
Answer: (E)  87.5%
Question: The volumes of two cones are in the ratio 1 : 20 and the radii of the cones are in the ratio of 1 : 5. What is the length of the wire?
(A) A)5:4
(B) B)2:7
(C) C)2:2
(D) D)2:1
(E) E)2:9
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/20 = (1)2h1/(5)2h2
=> h1/h2 = 5/4
i.e. h1 : h2 = 5 : 4
Answer: A
Answer: (A) A)5:4
Question: A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have ?
(A) 1000
(B) 1074
(C) 1075
(D) 1080
(E) 1089
Rationale: Explanation:
No. of digits in 1-digit page nos. = 1x9 = 9.
No. of digits in 2-digit page nos. = 2 x 90 = 180.
No. of digits in 3-digit page nos. = 3 x 900 = 2700.
No. of digits in 4-digit page nos. = 3189 - (9 + 180 + 2700) = 3189 - 2889 = 300.
Therefore No. of pages with 4-digit page nos. = (300/4) = 75.
Hence, total number of pages = (999 + 75) = 1074.
Answer: B
Answer: (B) 1074
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
(A) 12%
(B) 12.5%
(C) 13%
(D) 14%
(E) 14.5%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
B)
Answer: (B) 12.5%
Question: What is cost price of an article sold by a trader at 15% loss, given that the trader would have made a profit of 6% if he had sold it for $30 more?
(A) $576.19
(B) $436.19
(C) $476.19
(D) $470.19
(E) $276.19
Rationale: Let C.P. be $x
Then 106% of x - 85% of x = 100
21% of x = 100
21/100 *X = 100
21x = 10000
x = 476.19
Answer is C
Answer: (C) $476.19
Question: Mangala completes a piece of work in 20 days, Raju completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is?
(A) 8 days
(B) 12 days
(C) 14 days
(D) 16 days
(E) 18 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 20 × 30/50 = 12 days
B
Answer: (B) 12 days
Question: If the terms of a series are either2or24and the sum of all the terms F of the series is 124, then which of the following could be the number of2sin the series?
(A) 26
(B) 29
(C) 35
(D) 40
(E) 48
Rationale: Ans: A
Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms F is 124 means 24*5= 120 so number of 24 can't be more than 5
so 24x +2y = 124
24*5 + 2y =124 then y=2
24*4 + 2y = 124 then y=14
24*3 +2y = 124 then y= 26
24*2 +2y =124 then y = 38
24 +2y = 124 then y= 50
26 is the ans.A
Answer: (A) 26
Question: The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is
(A) 45
(B) 50
(C) 55
(D) 60
(E) 65
Rationale: Option A
Answer: (A) 45
Question: In the rectangular coordinate system, if the line x = 4y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
(A) 3
(B) 2
(C) 1/2
(D) 1/3
(E) 1/4
Rationale: x = 4y+5, and thus y = x/4 - 5/4
The slope is 1/4.
The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2
p/2 = 1/4 and thus p = 1/2
The answer is C.
Answer: (C) 1/2
Question: One out of every 500 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 14 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?
(A) 2,000
(B) 5,000
(C) 10,000
(D) 35,000
(E) 52,000
Rationale: out of 500 only 1 bulb is defective.So for 10 defective bulbs, we must have 5000 bulbs
Now out of these 10 bulbs, 2 bulbs, have broken glass
i.e 2 broken glass out of 5000 bulbs
14 broken glass will be from 35000 bulbs
Answer is D
Answer: (D) 35,000
Question: Annie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 10 years older than Larry, how old is Annie?
(A) 3
(B) 8
(C) 19
(D) 26
(E) 34
Rationale: J = L+10
(1) 2(A+3) = L+3
(2) 3(A+5) = J+5 = L+15
Let's subtract equation (1) from equation (2)
A+9 = 12
A = 3
The answer is A.
Answer: (A) 3
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 287 m
(B) 350 m
(C) 267 m
(D) 287 m
(E) 656 m
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer:B
Answer: (B) 350 m
Question: A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
(A) 100
(B) 110
(C) 128
(D) 134
(E) 156
Rationale: First Purchased = 250 Wes= 128
C
Answer: (C) 128
Question: The mean proportional between 4 and 16 is?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: root of(4*16)=2*4=16
ANSWER:E
Answer: (E) 16
Question: In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what X percentage of those asked favoured more than one of the 3 proposals.
(A)  10
(B)  12
(C)  17
(D)  22
(E)  30
Rationale: Bunuel, my answer for exactly 2 people was 17 and this was my approach:
100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to
X=100%=(50+30+20)-(at least 2 people)-5%+22%.C
Answer: (C)  17
Question: The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is?
(A) 3
(B) 5
(C) 7
(D) 11
(E) 13
Rationale: x + y = 25
xy = 144
(x- y)2 = (x + y)2 – 4xy
(x- y)2 = 625 – 576 => (x – y) = 7
ANSWER:C
Answer: (C) 7
Question: Max owns 200 shares of stock A and 180 of stock b. Last month the stocks had gained and lost the amounts shown below. What was Max's net gain or loss for the month?
Stock Gain/Loss
A 200 -18
B 180 40
(A) 3600
(B) -3600
(C) 7200
(D) 10800
(E) 438
Rationale: Find how much the gain or loss is and add all stocks together in the end.
Correct answer is A)3600
Answer: (A) 3600
Question: A can run 4.5 km distance in 1 min 30 seconds, while B can run this distance in 3 min. By how much distance can A beat B?
(A) 2250 m
(B) 1000 m
(C) 1250 m
(D) 1800 m
(E) 2000 m
Rationale: A takes time 1.30 minutes=90 sec
B takes time 3 minutes=180sec
diffrence= 180-90=90sec
now we are to find distance covered in 90 sec by B
180sec=4500m
1sec=25m
90sec=25x90=2250m
ANSWER:A
Answer: (A) 2250 m
Question: Which of the following equations describes a line that is perpendicular to y=x+4?
(A) y = x − 4
(B) y = −2 − x
(C) y = 4x
(D) y = 4x+1
(E) y = 1/x + 4
Rationale: Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y=x+4 is 1 so the slope of a perpendicular line will be -1.
The answer is B.
Answer: (B) y = −2 − x
Question: The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 5 years ago, the sum of their ages was 75, what will be the age of Aman 10 years from now?
(A) 17
(B) 25
(C) 27
(D) 35
(E) 40
Rationale: Let the present ages of Aman, Bren, and Charlie be 5x, 8x and 7x respectively.
5x-5 + 8x-5 + 7x-5 = 75
x = 3
Present age of Aman = 5*3 = 15
Aman's age 10 years hence = 15+10 = 25
Answer = B
Answer: (B) 25
Question: A man borrowed Rs.10000 from a lender at 9% p.a rate of interest. Find the amount to be paid by the man after 2years 6months?
(A) Rs 10050
(B) Rs 12050
(C) Rs 12250
(D) Rs 13000
(E) Rs 14550
Rationale: Principal = Rs 10000 Rate of interest R = 9%
T= 2 years 6 months= 2 ½ years=
5/2 years
Simple Interest=
PTR/100
= 10000 X
5/2 X 9/100
= Rs 2250
Amount= Prinipal + Simple interest = Rs 10000+ Rs 2250 = Rs 12250 C)
Answer: (C) Rs 12250
Question: The amount of water (in ml) that should be added to reduce 18 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 8 ml
(B) 5 ml
(C) 4 ml
(D) 6 ml
(E) 12 ml
Rationale: 9 9
30% 70%
30% ----- 9
70% ------? => 21 - 9 = 12 ml
Answer:E
Answer: (E) 12 ml
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
(A) 5/17
(B) 5/12
(C) 1/98
(D) 2/08
(E) 3/76
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer:B
Answer: (B) 5/12
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 35. Find the profit percentage?
(A) 80%
(B) 50%
(C) 75%
(D) 40%
(E) 53%
Rationale: L.C.M of 15 and 12
= 60
CP of 60 articles
= Rs. 100 (25 * 4)
SP of 60 articles
= Rs. 175 (35 * 5)
Profit percentage
= (175 - 100)/100 * 100 = 75%
Answer: C
Answer: (C) 75%
Question: If Tim had lunch at $50.50 and he gave 10% tip, how much did he spend?
(A) A)$57.45
(B) B)$35.42
(C) C)$60.60
(D) D)$55.55
(E) E)$78.45
Rationale: The tip is 10% of what he paid for lunch.
tip = 10% of 50.50 = (10/100)*50.50 = $5.05
Total spent
50.50 + 5.05 = $55.55
correct answer is D)$55.55
Answer: (D) D)$55.55
Question: Two pipes can fill a tank in 15 hours and 30 hours. While the 3rd pipe empties the full tank in 45hours. If all the 3 pipes are open in how much time will the tank be filled?
(A) 15/72
(B) 88/12
(C) 75/16
(D) 90/11
(E) 57/10
Rationale: Net part filled in 1 hour = 1/15 + 1/30 - 1/45 = 11/90
The tank will be full in 90/11 hr
Answer is D
Answer: (D) 90/11
Question: Cara and Dan drive at constant speeds toward each other on a highway. Cara drives at a constant speed of 32 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Cara is 110 km away from Dan at 7 am, and also 110 km away from Dan at 11 am, then how fast is Dan driving (in kilometers per hour)?
(A) 20
(B) 23
(C) 26
(D) 29
(E) 32
Rationale: Cara and Dan complete 220 km / 4 hours = 55 km/hour
Dan's speed is 55-32=23 km/hour
The answer is B.
Answer: (B) 23
Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
(A) 3/140
(B) 1/28
(C) 3/56
(D) 3/35
(E) 7/40
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.
Answer: E.
Answer: (E) 7/40