divelab/Sys2Bench huggingface dataset:
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?
Options:
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
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?
Options:
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
Question: If f(a)=2a+6, what is the value of (f(2a)+f(a)) ?
Options:
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
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?
Options:
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
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?
Options:
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
Question: 21 goats eat as much as 15 cows. How many goats eat as much as 35 cows?
Options:
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
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
Options:
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
Question: How many words can be formed by using all letters of the word ‘RIO’ ?
Options:
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
Question: What is the twenty-third decimal to the right in the fraction 23/24?
Options:
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
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?
Options:
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
Question: for which value of n, 4^85+2^3373+4^n will be the perfect square ??
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
Question: 8k8
+ k88
--------
1,6e6
If k and e represent non-zero digits within the integers above, what is e?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
Question: If p is even and q is odd, which of the following is odd?
Options:
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
Question: If x and y are positive integers and 20x=10y what is the least possible value of xy?
Options:
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
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?
Options:
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
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
Options:
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
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?
Options:
A)43
B)55
C)35
D)45
E)40
Rationale: 1200*(15/100) = 180 ---- 4
? ---- 1 => Rs.45
Answer:D
Answer: D
Question: How many positive integers less than 255 are multiple of 4 but NOT multiples of 6?
Options:
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
Question: Rice weighing 3power3/4 pounds was divided equally and placed in 4 containers. how many ounces of rice were in each?
Options:
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
Question: Without stoppages a train travels a certain distance with an average speed of 80 kmph and with stoppages it covers the same distance with an average speed of 40 kmph. What is the time in minutes per hour for which train stops?
Options:
A)26 min/hr
B)30 min/hr
C)32 min/hr
D)45 min/hr
E)12 min/hr
Rationale: Pick a smart number for the distance. lets say LCM 80
Without = 80/80 = 1 hours
With = 80/40= 2 hours
So in a trip of 2 hours, 1 hour is spent in stoppages
Hence, 60/2 = 30 min/hr on stoppages
Answer : B
Answer: B
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
Options:
A)4
B)6
C)0
D)9
E)19
Rationale: Answer: Option D
x/2 â€“ x/3 = 6 => x =6
3 + 6 = 9
Answer: D
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age one years back was?
Options:
A)10 years
B)12 years
C)14 years
D)16 years
E)18 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 1 years back (19 - 1) = 18 years.
E
Answer: E
Question: A river boat leaves Silver Town and travels upstream to Gold Town at an average speed of 6 kilometers per hour. It returns by the same route at an average speed of 5 kilometers per hour. What is the average speed for the round-trip in kilometers per hour?
Options:
A)5.5
B)7.1
C)7.2
D)7.0
E)8.0
Rationale: Pick a number which is LCM of 5 and 6 = 30.
Upstream time = 30/6 = 5 hrs
Downstream time = 30/5 = 6 hrs
Total time = 11 hrs
Total distance = 60
Average Speed = 60/11 = 5.5 km/hr
Answer: A
Question: Determine a man’s present age if his present age is 125% of his age 10 years ago and 83.333% of his age 10 years from now.
Options:
A)40 years
B)50 years
C)60 years
D)70 years
E)80 years
Rationale: Explanation:
According to the question current age of the man is:
1.	125% of his age 10 years ago
2.	83.333% of his age 10 years from now
Let the current age of the man be x.
Therefore, equating the two equations generated:
125/100(x-10) = 250/3(x+10)
x = 50
ANSWER B
Answer: B
Question: A boat can travel with a speed of 40km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 45km downstream.
Options:
A)1 hr
B)2 hrs
C)3 hrs
D)4 hrs
E)5 hrs
Rationale: Speed downstream = (40 + 5) km/hr = 45 km/hr.
Time taken to travel 45 km downstream = 45/45 hrs = 1 hrs.
Answer : A
Answer: A
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)299
B)278
C)245
D)265
E)123
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30
= 25/2 ==> 2(130 + X)
= 750 ==> X
= 245 m.
Answer:C
Answer: C
Question: Kathy has 34 tokens for the bus. She uses three tokens a week. How
many weeks can Kathy use the bus before she has to buy more tokens?
Options:
A)10 weeks-5 token
B)11 weeks-1 token
C)13 weeks-2 token
D)15 weeks-5 token
E)16 weeks-7 token
Rationale: 34/3 =11 R 1 Kathy will use her tokens for 11 weeks and she will have
one token left over.
correct answer B
Answer: B
Question: The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member.
Find how much younger is the new member ?
Options:
A)35
B)15
C)40
D)52
E)14
Rationale: C
Let the sum of nine member (total) =x
and the age of old one=z
so its average 4 yrs before=(x+z)/10.
after 4 yrs let z be replaced by y.
so now avg=(x+4*10+y)/10
now (x+z)/10=(x+40+y)/10
so after solving it found
z=y+40.
so old person is 40yrs older than young one.
Answer: C
Question: A coin is tossed 4 times. What is the probability z that the number of Heads is equal to the number of Tails?
Options:
A)1/8
B)1/4
C)3/8
D)1/2
E)9/16
Rationale: We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.
Using the binary formula and defining a head as a success,
P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2
= 6/16
z= 3/8
The answer is therefore (C)
Answer: C
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Options:
A)23 years
B)24 years
C)25 years
D)26 years
E)27 years
Rationale: EXPLANATION
Let the average age of the whole team by x years.
11x – (26 + 29) = 9(x -1)
11x – 9x = 46
2x = 46
x = 23.
So, average age of the team is 23 years.
Answer A
Answer: A
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?
Options:
A)62.5
B)62.9
C)62.8
D)62.1
E)62.2
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Answer: A
Question: Convert 300 inches into centimeter?
Options:
A)762cm
B)750cm
C)650cm
D)710cm
E)754cm
Rationale: 1 inch = 2.54cm
300 inches = 300*2.54 = 762cm
Answer is E
Answer: E
Question: On a certain Monday, Carlos drove to work at an average speed of 50 miles per hour and home from work along exactly the same route at an average speed of 60 miles per hour. Which of the following is closest to his average speed for both trips combined?
Options:
A)54.54
B)52
C)53
D)55
E)56
Rationale: To solve the average speed questions, we need to know the total distance and the total time.
Let us assume that the distance from work = D
This will also be the distance from work to home
Hence total distance travelled = 2D
Time in going to work = D/50,
Time in coming back from work = D/60
Hence average speed of both the trips = 2D/ (D/50 + D/60)
= 2*300/11 = 54.54
A
Answer: A
Question: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
Options:
A)766 cm2
B)535 cm2
C)285 cm2
D)324 cm2
E)235 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer:C
Answer: C
Question: What could be the range of a set consisting of odd multiples of 11?
Options:
A)21
B)24
C)44
D)62
E)70
Rationale: Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 11*(2n+1) where n is any positive integer.
Range = 11*(2m + 1) - 11*(2n + 1) = 11*2*(m-n) = 22 * (m-n).
m, n - any positive integers
The answer must be divisible by 22, which is only 44.
The correct answer is C
Answer: C
Question: A, B and C started a shop by investing Rs. 2,000, Rs. 6,000 and Rs. 2,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 300, then the total profit was :
Options:
A)30,000
B)60,000
C)80,000
D)1500
E)None
Rationale: Sol.
A : B : C = 2000 : 6000 : 2000 = 2: 6 : 2. so, Câ€™s share : Total Profit = 2 : 10.
Let the total profit be Rs. x. Then, 2/10 = 36000/x or x
= 300 * 10 / 2 = 1500
Answer D
Answer: D
Question: Ross has 40 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.
Options:
A)6 ; 10.
B)4 ; 25.
C)4 ; 10.
D)5 ; 25.
E)3 ; 10.
Rationale: Total shirts = 40
Green shirts = 3/4*40 = 30, Non green shirts = 10
Shirts without button = 1/10*40 = 4, shirts with button = 36
Required: Range of shirts with buttons that are not green.
Maximum non green shirts with buttons = number of non green shirts = 10
Minimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 10 - 4 = 6
Hence the range would be (6, 10)
Correct Option: A
Answer: A
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 312 votes. Find the number of votes casted to the winning candidate?
Options:
A)288
B)744
C)788
D)298
E)806
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 312
62% -------- ? => 806
Answer: E
Answer: E
Question: Ten women can do a work in six days. Six men can complete the same work in five days. What is the ratio between the capacity of a man and a woman?
Options:
A)1:2
B)2:1
C)2:3
D)3:2
E)None of these
Rationale: Explanation:
(10 × 6) women can complete the work in 1 day.
∴ 1 woman's 1 day's work = 1/60
(6 × 5) men can complete the work in 1 day.
∴ 1 man's 1 day's work = 1/30
so, required ratio =1/30 : 1/60= 2:1
Answer: B
Answer: B
Question: What is the sum of the different positive prime factors of 320?
Options:
A)7
B)10
C)15
D)17
E)21
Rationale: Prime factorization of 320
=32 * 10
=8*4 * 10
=2*4 * 2*2 * 2*5
=2* 2*2 * 2*2 * 2*5
=2^6 * 5
Sum of the different positive prime factors of 320 = 2+5
=7
Answer A
Answer: A
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 100. If legs are counted, there are 580. The number of hares in the zoo is?
Options:
A)210
B)182
C)190
D)137
E)371
Rationale: 100*2 = 200
580
-----
380
1----2
?----380 = 190
Answer:C
Answer: C
Question: What annual installment will discharge a debt of Rs. 1176 due in 3 years at 12% simple interest?
Options:
A)315
B)350
C)325
D)335
E)None of them
Rationale: Let each Installment be Rs. x
Then, ( x+ ((x*12*1)/100)) + (x+ ((x*12*2)/100) ) + x = 1176
=((28x/25) + (31x/25) + x) = 1176 ïƒ› (28x+31x+25x)=(1176*25)
x= (1176*25)/84 = Rs.350.
Therefore,	Each installment = Rs. 350.
Answer is B.
Answer: B
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
Options:
A)45
B)60
C)75
D)90
E)95
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90
Answer: Option D
Answer: D
Question: A is three years older than B who is thrice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
Options:
A)10 years
B)12 years
C)14 years
D)15 years
E)8 years
Rationale: Let C's age be x years. Then, B's age = 3x years. A's age = (3x + 3) years.
(3x + 3) + 3x + x = 31
7x = 28
x = 4.
Hence, B's age = 2x = 8 years.
E)
Answer: E
Question: Suganya and Suriya are partners in a business. Suganya invests Rs. 32,000 for 8 months and Suriya invests Rs.28,000 for 10 months. Out of a profit of Rs.30,570. Suganya's share is
Options:
A)Rs.9471
B)Rs.12,628
C)Rs.912.54
D)Rs.18,942
E)None
Rationale: Solution
Ratio of their shares	=(32000Ã—8):(28000Ã—10)
= 32:35 .
Suganya's share	= Rs.(31570 Ã—2/67)
= Rs.912.54.
Answer C
Answer: C
Question: John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment E that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
Options:
A)a. 3/5
B)b.2/3
C)c.7/10
D)d.3/4
E)e.4/5
Rationale: X(10) --- Net(0) --- E(-15) = -15/-10 = 3/2.
So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
Answer: A
Question: There are 24 students in Chadâ€™s class. He brought 25 cookies to pass out
for his birthday. How many cookies will each student get? Will there be
any cookies left over?
Options:
A)1-9
B)1-7
C)2-8
D)1-1
E)3-10
Rationale: 25/24 = 1 R 1 Chad will give each student 1 cookie and there will be 1
cookies left over
correct answer D
Answer: D
Question: John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least?
Options:
A)John
B)Susan
C)Sam
D)Mark
E)Lynn
Rationale: John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 160% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);
As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.6*J)=0.8*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John.
Answer: B.
Answer: B
Question: The least common multiple of positive integer m and 3-digit integer n is 690. If n is not divisible by 3 and m is not divisible by 2, what is the value of n?
Options:
A)115
B)230
C)460
D)575
E)690
Rationale: The LCM of n and m is 690 = 2*3*5*23.
m is not divisible by 2, thus 2 goes to n
n is not divisible by 3, thus 3 goes to m.
From above:
n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23 = 230.
Answer: B.
Answer: B
Question: A student was asked to find 4/5 of a number. But the student divided the number by 4/5, thus the student got 27 more than the correct answer. Find the number.
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Let the number be x.
(5/4) * x = (4/5)*x + 27
25x = 16x + 540
9x = 540
x = 60
The answer is C.
Answer: C
Question: Find the next number in the Sequence
3, 8, 23, 48, ?
Options:
A)88
B)84
C)85
D)83
E)81
Rationale: +5 =>8
+15 =>23
+25 =>48
+35 =>83
Answer is D
Answer: D
Question: A library has an average of 150 visitors on sundays and 120 on other days . The avearge number of visitors per day in a month of 30 days beginning with a sunday is?
Options:
A)50
B)75
C)150
D)125
E)100
Rationale: Since the month begin with sunday, so there will be five sundays in the month
Required average = (150*5 + 120*25)/30 = 3750/30 = 125
Answer is D
Answer: D
Question: A fold density is 19 times greater than the water and for copper it is 9 times. At what ratio you can mix gold
and copper to get 15 times denser than water. ?
Options:
A)3 : 1
B)3 : 2
C)3 : 5
D)3 : 8
E)3 : 7
Rationale: Suppose x units of gold are mixed with y units of copper to make (x+y) units of alloy which is 15 times denser than water.
Then 19*x + 9*y = 15*(x + y)
=> 19*x - 15*x = 15*y - 9*y
=> 4*x = 6*y => x/y = 3/2
So gold and copper should be mixed respectively in the ratio of 3 : 2
ANSWER:B
Answer: B