mathewhe/aqua_rat huggingface dataset:
Question: A runs twice as fast as B and gives B a start of 83m.How long should the racecourse be so that A and B might reach in the same time?
(A) 75 m.
(B) 80 m.
(C) 150 m.
(D) 100 m.
(E) None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 83m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 83m is 83/1=83m
so the total time taken by a and b to reach =2*83=166m
ANSWER:E
Answer: (E) None of the above
Question: What is the square root of 5,625?
(A) A)18
(B) B)75
(C) C)45
(D) D)62
(E) E)81
Rationale: A square root of a number is a number times itself equals the original number.
Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).
75*75=5,625
5625 divided by x = 75
x=75
(B)75
Answer: (B) B)75
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 40
(B) 44
(C) 48
(D) 47
(E) 50
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
ANSWER B
Answer: (B) 44
Question: From among the 38 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
(A) 1360
(B) 1260
(C) 1060
(D) 1160
(E) 1406
Rationale: There are 38 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 38 ways. When one person is appointed as leader, we are left with 35 students. Out of these 37 teachers, we can select one class representative. So, a class representative can be selected in 37 ways. Hence, the number of ways in which a leader and class representative can be selected = 38 x 37 = 1406
ANSWER:E
Answer: (E) 1406
Question: The H.C.F. of two numbers is 40 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
(A) 276
(B) 600
(C) 699
(D) 722
(E) 745
Rationale: the numbers are (40 x 11) and (40 x 15).
Larger number = (40 x 15) = 600.
ANSWER :B
Answer: (B) 600
Question: A bus trip of 450 miles would have taken 1 hour less if the average speed S for the trip had been greater by 5 miles per hour. What was the average speed S, in miles per hour, for the trip?
(A) 10
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: (S+5)(T-1) = 450
S*T = 450
Solving both the equations, we get: S = 45 or -50
Since Speed should be positive, S = 45
Hence, option C
Answer: (C) 45
Question: If k is an integer and 0.00010101 x 10^k is greater than 1000, what is the least possible value of k?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: 0.00010101 * 10^k > 1000
We need to move the decimal point to the right 7 places to get 1010.1
This is equivalent to multiplying by 10^7.
The answer is B.
Answer: (B) 7
Question: If 7/w + 7/x = 7/y and wx = y, then the average (arithmetic mean) of w and x is
(A) 1/2
(B) 1
(C) 2
(D) 4
(E) 8
Rationale: Given: 7/w + 7/x = 7/ywx=y
Find: (w+x)/2 = ?
7(1/w + 1/x) = 7(1/y) - divide both sides by 7
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1
Therefore (w+x)/2 = 1/2
Ans: A
Answer: (A) 1/2
Question: #88
A necklace is made by stringing N individual beads together in the repeating pattern red bead, ORANGE bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then N could equal
(A) 16
(B) 32
(C) 41
(D) 48
(E) 64
Rationale: You can just write out the pattern and count: RGWBYRGWBYRGWBY... But to save time a good test taker will just look for a pattern. Min # is 3, because W is the third one. Then every 5 beads another white comes, so it must be 3+5+5+5.. and so on...
3+5 = 8
3+5+5 = 13
3+5+5+5=18
3+5+5+5+5=23
So you see it ends in either 8 or 3. Pick an answer that ends in either 8 or 3. Only one answer does, D.
Answer: (D) 48
Question: There are between 120 and 130 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
(A) 121
(B) 123
(C) 125
(D) 127
(E) 129
Rationale: The numbers with the form 4n+1 are 121, 125, and 129.
Only 125 has the form 3k+2.
The answer is C.
Answer: (C) 125
Question: An automobile manufacturer offers a station wagon with either a 16-cylinder engine or a 14-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 16-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?
(A)  192
(B)  128
(C)  64
(D)  56
(E)  44
Rationale: 16-cylinder engine wagons = 2*2*2*2*2*2*2 = 128 (manual or automatic, with or without trailer);
14-cylinder engine wagons = 2*2*2*2*2*2 = 64 (manual or automatic).
Total = 128 + 64 = 192.
Answer: A.
Answer: (A)  192
Question: In an IT company, there are a total of 90 employees including 50 programmers. The number of male employees is 80, including 35 male programmers. How many employees must be selected to guaranty that we have 3 programmers of the same sex?
(A) 10
(B) 45
(C) 55
(D) 35
(E) 65
Rationale: You could pick 40 non-programmers, 2 male programmers, and 2 female programmers, and still not have 3 programmers of the same sex. But if you pick one more person, you must either pick a male or a female programmer, so the answer is 45.
B
Answer: (B) 45
Question: If x is an integer, and 144 < x^2 <= 361, which of the following is the sum of all possible values of x?
(A)  135
(B)  124
(C)  116
(D) None of the above
(E)  105
Rationale: The range of x is from 13 .. to 19 and -13 to -19 so the sum is 0 hence ans D, I guess, unless I am missing something!
Answer: (D) None of the above
Question: The number of singles that a baseball player hit increased 15 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 5 percent. If the total number of singles and doubles that she hit increased 4 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?
(A) 3:5
(B) 5:7
(C) 7:11
(D) 9:11
(E) 11:15
Rationale: Soln:-
1.15S + 0.95D = 1.04[S + d]
0.11S = 0.09D
S/D = 9/11
ANSWER:D
Answer: (D) 9:11
Question: How many ways are there to split a group of 4 boys into two groups of 2 boys each? (The order of the groups does not matter)
(A) 5
(B) 6
(C) 7
(D) 3
(E) 8
Rationale: the combination is 4C2 /2
= 4!/2!*2! *2 = 3
D
Answer: (D) 3
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) Rs.547
(B) Rs.519
(C) Rs.520
(D) Rs.540
(E) Rs.529
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer:D
Answer: (D) Rs.540
Question: In a 1400 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?
(A) 100 sec.
(B) 70 sec
(C) 25 sec
(D) Data not sufficient
(E) None of these
Rationale: Speed of Shiny = 50/ 10 = 5m/s
Time taken by shiny to complete the race is B = 1400/5 = 280 sec.
Time taken by Baley to complete the race is D = 1400/4 = 350 sec.
Hence, D-B = 70 sec
ANSWER:B
Answer: (B) 70 sec
Question: A room contains 140 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 10
(B) 35
(C) 40
(D) 60
(E) 80
Rationale: Say group of x people left the room.
# of women in the room was 0.15*140=21;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(140-x);
So, 21-0.3x= 0.1(140-x) --> x=35.
Answer: B.
Answer: (B) 35
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 5 percent during the third year. What is the value of the account today?
(A) $10,350
(B) $10,972.50
(C) $10,500
(D) $11,500
(E) $12,705
Rationale: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.95 = 10,395
Answer B is correct.
Answer: (B) $10,972.50
Question: What is the greatest possible length which can be used to measure exactly the lengths 8 m, 4 m 20 cm and 12 m 20 cm?
(A) 10 cm
(B) 30 cm
(C) 25 cm
(D) 20 cm
(E) 35 cm
Rationale: Required length
= HCF of 800 cm, 420 cm, 1220 cm
= 20 cm
Answer: Option D
Answer: (D) 20 cm
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
(A) 17/25
(B) 17/24
(C) 17/23
(D) 17/20
(E) 17/21
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: (D) 17/20
Question: Aishwarya’s mom was 42 years of age at the time of her birth, while her mom was 32 years old when her 4 years younger sister was born. The variance between the parents ages is :
(A) 6 years
(B) 14 years
(C) 10years
(D) 9 years
(E) 4 years
Rationale: B
14 years
Mom’s age when Aishwarya’s sister was born = 32 years.
Dad’s age when Aishwarya’s sister was born = (42 + 4) years = 46 years.
Needed Variance = (46 – 32) years = 14 years.
Answer is B
Answer: (B) 14 years
Question: If x = a!, which of these following values of a is the least possible value (in this list) for which the last 7 digits of the integer x will all be zero?
(A) 28
(B) 32
(C) 36
(D) 40
(E) 44
Rationale: 2*5 will give one 0 at the end. We need 2^7*5^7 to get 7 zeroes at the end.
There are many 2's, so we need to find the first 7 appearances of 5.
These multiples of 5 are: 5, 10, 15, 20, 5*5, 30...which gives us 7.
To have at least 7 zeroes at the end, a => 30.
The answer is B.
Answer: (B) 32
Question: By selling 80 bananas, a fruit-seller gains the selling price of 10 bananas. Find the gain percent?
(A) 25.32%
(B) 17.46%
(C) 15.55%
(D) 14.28%
(E) 56.25%
Rationale: SP = CP + g
80 SP = 80 CP + 10 SP
70 SP = 80 CP
70 --- 10 CP
100 --- ? => 14.28%
Answer: D
Answer: (D) 14.28%
Question: In a simultaneous throw of two dice , what is the probability of getting to total of 10 or 11?
(A) 5/4
(B) 9/8
(C) 4/11
(D) 5/36
(E) 7/52
Rationale: n(S)36
n(E)=5
P(E)=5/36
Ans: D
Answer: (D) 5/36
Question: On a certain date, Pat invested $9,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $36,000, in how many years total will the total value of the investment plus interest increase to $72,000?
(A) 15
(B) 16
(C) 18
(D) 20
(E) 24
Rationale: 36,000 = 9,000(1 + x)^10
4 = (1+x)^10 = 2^2
(1+x)^10 = ((1+x)^5)^2 = 2^2
Therefore, (1+x)^5 = 2
72,000 = 9,000(1 + x)^n
8 = (1+x)^n
2^3 = (1+x)^n
(1+x)^n = ((1+x)^5)^3 = (1+x)^15
Therefore, n = 15.
The answer is A.
Answer: (A) 15
Question: A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability W that the sum of the three numbers on the balls selected from the box will be odd?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);
P(OOO)=(1/2)^3;
P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE);
So finally W=1/8+3/8=1/2.
Answer: C.
Answer: (C) 1/2
Question: Find the odd man out
2, 3, 12, 37, 86, 166, 288
(A) 2
(B) 3
(C) 86
(D) 116
(E) 126
Rationale: 2+(1)^2=3
3+(3)^2=12
12+(5)^2=37
37+(7)^2=86
86+(9)^2=167
167+(11)^2=288
ANSWER:D
Answer: (D) 116
Question: A worker earns $24 on the first day and spends $18 on the second day. The worker earns $24 on the third day and spends $18 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $48?
(A) 6
(B) 7
(C) 9
(D) 12
(E) 16
Rationale: Every two days, the net total is $6.
After 8 days, the worker will have $24.
On day 9, the worker will receive $24 for a net total of $48.
The answer is C.
Answer: (C) 9
Question: Two trains leave the same train station at 6:00 am and 6:45 am and they travel at 100 kph and 120 kph respectively. How many kilometers from the train station will the two trains be together?
(A) 420
(B) 450
(C) 480
(D) 510
(E) 540
Rationale: At 6:45, the first train is 75 km ahead.
The second train gains 20 km each hour.
The time it takes the second train to catch the first train is 75 /20 = 3.75 hours.
In this time, the second train travels 3.75*120=450 km.
The answer is B.
Answer: (B) 450
Question: A small pool filled only with water will require an additional 700 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 700 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
(A) 1000
(B) 1250
(C) 1300
(D) 1600
(E) 2125
Rationale: Since pumping in additional 700 gallons of water will increase the amount of water in the pool by 30%, then initially the pool is filled with 1,000 gallons of water.
So, we have that 1,000 + 700 = 0.8*{total} --> {total} = 2,125.
Answer: E.
Answer: (E) 2125
Question: If b is a positive integer, which of the following could NOT be the square of b?
(A) 3165
(B) 9436
(C) 4726
(D) 6445
(E) 1432
Rationale: A number ending in 2 cannot be a perfect square.
1432 ends in a number 2, making that the correct answer
(E) 1432
Answer: (E) 1432
Question: A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,587.75. How many boxes of plain cookies did she sell?
(A) 0
(B) 233
(C) 500
(D) 695
(E) 787
Rationale: Let #plain cookies sold be X then #chocolate cookies = (total cookies-X)
Equating for X
(0.75)*X +(1.25)*(1585-X)=1587.75
=>x=787
E
Answer: (E) 787
Question: A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is
(A) 1:3
(B) 4:3
(C) 2:3
(D) 2:1
(E) 3:1
Rationale: Explanation :
Work done by 20 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16×20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×16)
Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20
= 1/3 :1/4 = 4:3
Answer : Option B
Answer: (B) 4:3
Question: The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.6,040 for a cell phone, then what was the cost price of the cell phone?
(A) Rs.5,845
(B) Rs.6,750
(C) Rs.5,700
(D) Rs.4,910
(E) None of these
Rationale: Explanation:
123% of CP =SP
Therefore, CP = Rs.6,040x100/123 = Rs.4910
Answer: Option D
Answer: (D) Rs.4,910
Question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
(A) 13
(B) 18
(C) 40
(D) 37
(E) 25
Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C
Answer: (C) 40
Question: A bag contains 50p, 25p and 10p coins in the ratio 3 : 7 : 4, amounting to Rs. 109.50. Find the number of coins of each type.
(A) 80,250,140
(B) 75,220,135
(C) 90,210,120
(D) 80,210,120
(E) None of these
Rationale: Solution:
Let the number of 50p, 25p and 10p coins be 3x,7x and 4x respectively.
Then, 3x/2 + 7x/4 + 4x/10 = Rs. 109.50.
=> (30x + 35x + 8x)/20 = 109.50. => 73x = 109.5 * 20 => 73x =2190.
=> x =2190/73 = 30.
.'. number of 50p coins = 3*30 =90; number of 25p coins = 7*30 =210;
number of 10p coins = 4*30 =120.
ANSWER IS C
Answer: (C) 90,210,120
Question: 30 square stone slabs of equal size were needed to cover a floor area of 58.8 sq.m. Find the length of each stone slab?
(A) 140cm
(B) 767cm
(C) 88cm
(D) 666cm
(E) 776cm
Rationale: Area of each slab
=58.8/30m2=1.96m2
Length of each slab √1.96=1.4m=140cm
Answer: (A) 140cm
Question: What is the greatest 5-digit number when divided by 9 and 10 leaves a remainder of 7 and 9 respectively?
(A) 56780
(B) 78910
(C) 97479
(D) 97918
(E) 97929
Rationale: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 9 when we divide by 10, so E is the only possible answer.
Answer: (E) 97929
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 6 min
(B) 8 min
(C) 7 min
(D) 9 min
(E) 1 min
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) = 6 min.
So, the tank will be emptied in 6 min.
Answer: A
Answer: (A) 6 min
Question: A certain stock exchange designates each stock with a two-letter or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes without using the vowels A, E, I, O, or U?
(A) 9372
(B) 9482
(C) 9592
(D) 9702
(E) 9812
Rationale: The number of two-letter codes is 21*21=441.
The number of three-letter codes is 21*21*21=9261.
The total number of codes is 441+9261=9702.
The answer is D.
Answer: (D) 9702
Question: What is the least number of square tiles required to pave the floor of a room 10 m 17 cm long and 9m 9 cm broad?
(A) 724
(B) 804
(C) 11413
(D) 844
(E) None
Rationale: Solution
Length of largest tile = H.C.F. of 1017cm & 909cm = 9cm.
Area of each tile = (9 x 9)cm2
∴ Required number of tiles	= [1017x909/9x9]
= 11413.
Answer C
Answer: (C) 11413
Question: In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
(A) 5 balls.
(B) 9 balls.
(C) 10 balls.
(D) 7 balls.
(E) 6 balls.
Rationale: Let us first find the fraction of green, blue and yellow balls
1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator
= 11 / 24 , add numerators
The fraction of white balls is given by
24 / 24 - 11 / 24 = 13 / 24
So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then
(13 / 24) of x = 26 balls
or (13 / 24) ? x = 26
x = 26 ? (24 / 13) = 48 , total number of balls
The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by
(1 / 8) of 48 = 6 balls.
correct answer E
Answer: (E) 6 balls.
Question: Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 32
(B) 88
(C) 77
(D) 99
(E) 75
Rationale: Average = (76 + 65 + 82 + 67 + 85)/5 = 375/5 = 75.
Answer: E
Answer: (E) 75
Question: The average (arithmetic mean) of four numbers is 4x + 2. If one of the numbers is x, what is the average of the other three numbers?
(A) x + 1
(B) 3x + 3
(C) 5x + 1
(D) 5x + 8/3
(E) 15x + 12
Rationale: If the average of four numbers is 4x + 3, then the sum of all four numbers if 4 * (4x + 2) = 16x + 8. If one of the numbers is x, then the average of the remaining three numbers would be: (16x + 8 - x)/3 = (15x + 8)/3 = 5x + 8/3.
Answer is D.
Answer: (D) 5x + 8/3
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
(A) 33/01
(B) 33/91
(C) 33/90
(D) 33/99
(E) 83/98
Rationale: Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91
Answer: Option B
Answer: (B) 33/91
Question: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 600 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?
(A) 1.74%
(B) 1.94%
(C) 10%
(D) 15%
(E) 19%
Rationale: I think there is a typo in question.
It should have been "By weight Liquid 'X ' makes up..... "
Weight of Liquid X = 0.8 % of Weight of A + 1.8% of Weight of B
When 600gms of A and 700gms of B is mixed :
Weight of Liquid X = (0.8 * 600)/100 + (1.8* 700)/100 = 17.4gms
% of Liquid X in resultant mixture = (17.4/1000) *100 = 1.74%
A
Answer: (A) 1.74%
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years, The age of the 15th student is
(A) 17
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Age of the 15th student = [15 * 15 - (14 * 8 + 16 * 6)] = 17 years. Answer: A
Answer: (A) 17
Question: Working together at their respective constant rates, Machine A and Machine B can produce 1,600 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 1,600 unit total would it produce?
(A) 25
(B) 33
(C) 50
(D) 67
(E) 75
Rationale: 1/A+1/B= 1/T
1/A +1/12= 1/8 (50% more of 8 is 12)
1/A= 1/24
Machine A can produce 1600 units in 24 hrs, so it can produce 1600*8/24= 533.33 units is 8 hrs.
533.33 is 33.33% of 1600.
B is the answer
Answer: (B) 33
Question: Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length D of time will elapse before they chime together again?
(A) 2 hr. and 24 min.
(B) 4 hr. and 48 min.
(C) 1 hr. and 36 min.
(D) 5 hr.
(E) 2 hr.
Rationale: It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.
So the LCM of the three time intervals (18, 24,32) would be the answer.
LCM (18, 24, 32) D= 288 => 4 hours 48 mins.B
Answer: (B) 4 hr. and 48 min.
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
(A) Rs.18
(B) Rs.47
(C) Rs.44
(D) Rs.28
(E) Rs.28
Rationale: π (152 - 132) = 176
176 * 1/4 = Rs.44
Answer: C
Answer: (C) Rs.44
Question: Peter takes a loan of $100,000 with 12% annual interest: the interest is paid once, at the end of the year. Martha takes a loan of $100,000 with 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's loan interest, approximately how much more does Martha have to repay?
(A) $68.25
(B) Zero
(C) $6825.00
(D) $6.82
(E) $682.50
Rationale: Peters interest= $100,000*0.12 = $12,000 or $1,000 each month.
Martha’s interest, 12%/12 = 1% each month:
For the 1st month = $100,000*0.01 = $1,000;
For the 2nd month = $1,000 + 1% of 1,000 = $1,010, so we would have interest earned on interest (very small amount);
For the 3rd month = $1,010 + 1% of 1,010 = ~$1,020;
For the 4th month = $1,020 + 1% of 1,020 = ~$1,030;
...
For the 12th month = $1,100 + 1% of 1,100 = ~$1,110.
The difference between Peters interest and Martha’s interest = ~(10 + 20 + ... + 110) = $660.
Answer: E.
Answer: (E) $682.50
Question: What is the remainder when 1041*1047*1050*1053 is divided by 33?
(A) 3
(B) 27
(C) 30
(D) 21
(E) 18
Rationale: take the remainder from each of 1041/33, 1047/33 and so on..
1044/33 gives remainder = 18
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e = 18*24*27*30
break them into pairs 18*24/33 gives remainder 3
and 27*30/33 gives remainder 18
so 3*18/33 gives remainder 21.
D
Answer: (D) 21