mathewhe/aqua_rat huggingface dataset:
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?
(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) 30 min/hr
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
(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) 9
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?
(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) 18 years
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?
(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) 5.5
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.
(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) 50 years
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.
(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) 1 hr
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(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) 245
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?
(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) 11 weeks-1 token
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 ?
(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) 40
Question: A coin is tossed 4 times. What is the probability z that the number of Heads is equal to the number of Tails?
(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) 3/8
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?
(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) 23 years
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) 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) 62.5
Question: Convert 300 inches into centimeter?
(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) 754cm
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?
(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) 54.54
Question: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
(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) 285 cm2
Question: What could be the range of a set consisting of odd multiples of 11?
(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) 44
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 :
(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) 1500
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.
(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) 6 ; 10.
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?
(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) 806
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?
(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) 2:1
Question: What is the sum of the different positive prime factors of 320?
(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) 7
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?
(A) 210
(B) 182
(C) 190
(D) 137
(E) 371
Rationale: 100*2 = 200
580
-----
380
1----2
?----380 = 190
Answer:C
Answer: (C) 190
Question: What annual installment will discharge a debt of Rs. 1176 due in 3 years at 12% simple interest?
(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) 350
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?
(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) 90
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?
(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) 8 years
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
(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) Rs.912.54
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?
(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) a. 3/5
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?
(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) 1-1
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?
(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) Susan
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?
(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) 230
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.
(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) 60
Question: Find the next number in the Sequence
3, 8, 23, 48, ?
(A) 88
(B) 84
(C) 85
(D) 83
(E) 81
Rationale: +5 =>8
+15 =>23
+25 =>48
+35 =>83
Answer is D
Answer: (D) 83
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?
(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) 125
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. ?
(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) 3 : 2
Question: Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7200 km and comes back to the starting point. The total time taken by him is:
(A) 914.2 hours
(B) 900 hours
(C) 915 hours
(D) 905 hours
(E) 915 hours
Rationale: Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7200/18 + 7200/14 = 400 + 514.2 = 914.2 hours
Answer: Option A
Answer: (A) 914.2 hours
Question: The number of arrangements that can be made with the letters of the word MEADOWSS so that the vowels occupy the even places?
(A) 14
(B) 144
(C) 720
(D) 992
(E) 221
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 5 places in 5! i.e., 120 ways.
Hence the total ways are 120 * 6 = 720.
Answer:C
Answer: (C) 720
Question: What should come in place of the question mark (?) in the following equation?
45789+ 34567 = 610+ ?
(A) 96543
(B) 13678
(C) 23456
(D) 56789
(E) 79746
Rationale: 45789+ 34567 = 610+ ?
45789+ 34567 – 610 = 79746
Answer E
Answer: (E) 79746
Question: Today is Monday.After 61 days,it will be
(A) Wednesday
(B) Saturday
(C) Tuesday
(D) Thursday
(E) None of these
Rationale: Solution
Each day of the week is repeated after 7 days
So,after 63 days,it will be Monday.
∴ After 61 days,it will be Saturday. Answer B
Answer: (B) Saturday
Question: If 2 men or 3 women can reap a field in 8 days how long will 3 men and 4 women take to reap it?
(A) 2/16
(B) 1/16
(C) 3/24
(D) 5/16
(E) 6/26
Rationale: Explanation:
2 men reap 1/8 field in 1 day
1 man reap 1/(2 x 8)
3 women reap 1/8 field in 1 day
1 woman reap 1/(3 x 8)
3 men and 4 women reap (3/(2 x 8)+ 4/(3 x 8)) =5/16 in 1 day
3 men and 4 women will reap the field in 5/16 days
Answer: Option D
Answer: (D) 5/16
Question: If x is an integer, then x(x – 1)(x – k) must be evenly divisible by 4 when k is any of the following values EXCEPT
(A) -4
(B) -3
(C) -1
(D) 2
(E) 5
Rationale: We have the product of 3 integers: (x-1)x(x-k).
Note that the product of 3 integers is divisible by 4 if at least one multiple is divisible by 4. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 4 these numbers must have different remainders upon division by 4, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 2.
Next, if k=-3 then we'll have (x-1)x(x+2)=(x-1)x(x+3) --> which means that (x-1) and (x+3) will have the same remainder upon division by 4. Thus for k=-3 we won't be sure whether (x-1)x(x-k) is divisible by 4.
Answer: B.
Answer: (B) -3
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 5m3 , then the rise in the water level in the tank will be:
(A) 31.25 cm
(B) 25 cm
(C) 35 cm
(D) 50 cm
(E) None of these
Rationale: Explanation:
Total volume of water displaced =(5 x 50) m3 = 250 m3
Rise in water level = 250/40Ã—20= 0.3125m = 31.25cm
Answer: A
Answer: (A) 31.25 cm
Question: In how many ways can the letters of the word 'PRAISE' be arranged. So that vowels do not come together?
(A) 720
(B) 576
(C) 440
(D) 144
(E) None of these
Rationale: Required number of possible outcomes
= Total number of possible outcomes – Number of possible outcomes in which all vowels are together
= 6! – 4 ! × 3! = 576
Answer B
Answer: (B) 576
Question: What is the remainder when 1271 * 1275 * 1277 *1289 is divided by 12?
(A)  0
(B)  1
(C)  9
(D)  11
(E)  7
Rationale: 1271*1275*1277*1285 = (1272 - 1)(1272 + 3)(1284 - 7)(1284 + 5) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)
Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-1)(3)(-7)(5) = 105. Thus the question becomes: what is the remainder upon division of 105 by 12? The answer to this question is 9.
Answer: C.
Answer: (C)  9
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 70, the dividend is:
(A) A)5322
(B) B)5330
(C) C)12320
(D) D)53400
(E) E)53420
Rationale: Divisor = (5 * 70) = 350
= 10 * Quotient = Divisor
=> Quotient = 350/10 = 35
Dividend = (Divisor * Quotient) + Remainder
Dividend = (350 * 35) + 70 = 12320.
C
Answer: (C) C)12320
Question: A class consists of 6 boys and 5 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?
(A) 50
(B) 18
(C) 32
(D) 60
(E) 240
Rationale: Easiest way is to treat it like an arrangements question in the following manner:
From the boys we need to select 2 to be clown and pet: This can be done in 5*6 ways
Similarly for the girls, we have 4*5 ways.
Thus total = 30+20 = 50 ways. Thus A is the correct answer.
Answer: (A) 50
Question: The value of land increases by u% during June and decreases by v% during July. If the value of the land is the same at the end of July as at the beginning of June, what is v in terms of u?
(A) 200u/(100+2u)
(B) 100u/(100+u)
(C) u(2+u)/(1+u)2
(D) u(200+u)/10000
(E) 2u/u+2u
Rationale: The simplest pairing is a 25% increase will be offset by a 20% decrease.
Here's the proof:
Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100
So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...
Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.
Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.
Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.
Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.
Answer E: (50/25) + 50 = 52. ELIMINATE E.
ans B
Answer: (B) 100u/(100+u)
Question: A cricket bat is sold for $900, making a profit of $100. The profit percentage would be
(A) 24%
(B) 12.5%
(C) 30%
(D) 36%
(E) 40%
Rationale: 100/(900 - 100) = 100/800 = 0.125 = 12.5%.
Answer: B
Answer: (B) 12.5%
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12 m
(B) 888.88 m
(C) 777.52 m
(D) 756.34 m
(E) 766.34 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
ANSWER:A
Answer: (A) 111.12 m
Question: The average weight of A, B and C is 75 kg. If the average weight of A and B be 88 kg and that of B and C be 72 kg, then the weight of B is:
(A) 60 kg
(B) 59 kg
(C) 62 kg
(D) 63 kg
(E) 61 kg
Rationale: EXPLANATION
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (75 x 3) = 225 â€¦. (i)
A + B = (88 x 2) = 176 â€¦. (ii)
B + C = (72 x 2) = 144 â€¦.(iii)
Adding (ii) and (iii), we get: A + 2B + C = 288 â€¦. (iv)
Subtracting (i) from (iv), we get : B = 63.
Bâ€™s weight = 63 kg.
Answer D
Answer: (D) 63 kg
Question: Tough and Tricky questions: Work/Rate Problems.
If it takes 60 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job?
(A) 40/3
(B) 11
(C) 6
(D) 7/3
(E) 9/7
Rationale: 60 Workers = 3 hours then,
1 Worker = 3*60 Hours
30 Workers = (3*60) /(30) = 6 Answer.C
Answer: (C) 6
Question: A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work , how much time shall B take to do it ?
(A) 30 days
(B) 35 days
(C) 40 days
(D) None of these
(E) Cannot be determined
Rationale: Solution
Suppose B taken x days to do the work.
∴ A takes (2 x 3/4x) =2x/2 days to do it.
(A + B)'s 1 days work = 1/8.</p><p>
therefore 1/x + 2/3x -1/18 or x=30
Answer A
Answer: (A) 30 days
Question: A man has some hens and cows. If the number of heads be 50 and the number of feet equals 140, then the number of hens will be:
(A) 22
(B) 23
(C) 24
(D) 30
(E) 28
Rationale: let hens be x and cows be y
now,
feet: x*2+y*4=140
heads: x*1+y*1=50
implies, 2x+4y=140 and x+y=50
solving these two equations, we get x=30 and y=20
Therefore, hens are 26.
ANSWER:D
Answer: (D) 30
Question: There is a five-digit number. The fifth digit is one fourth of the third digit and one half of the fourth digit. Third digit is one half of the first digit. Second digit is 5 more than the fifth digit. What is that 5-digit number?
(A) 86421
(B) 86424
(C) 89421
(D) 96421
(E) 76421
Rationale: we can prove it as follows
suppose number is pqrst, now
t=(1/4)r=(1/2)s......(1),r=(1/2)p.....(2),q=t+5....(3)
now from (1)4t=r=2s=k(suppose)....(4)
from (2) 2r=p...(5)
now(4)*2 then we get 8t=2r=4s=k(again some integer)....(6)
from (5) and (6)
8t=2r=4s=p=k.........(7)
now we have to choose the value of k
1)if choose k=0 then it is worthless number will be 00000(not a answer)
2)for k=1 to 7 and for k=9 digits will be in fractions
3)for k=8 we get p=8,s=2,r=4,t=1 and q=6
and number is pqrst=86421
ANSWER:A
Answer: (A) 86421