mathewhe/aqua_rat huggingface dataset:
Question: If 10 litres of an oil of Rs.50 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre?
(A) Rs.49.17
(B) Rs.51.03
(C) Rs.54.17
(D) Rs.55.33
(E) None of the above
Rationale: 50*10 = 500
66*5 = 330
830/15 = 55.33
ANSWER:D
Answer: (D) Rs.55.33
Question: In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 300 points, how many points is the third question worth?
(A) 22
(B) 24
(C) 26
(D) 20
(E) 28
Rationale: x
x+4
x+8
x+12
x+16
x+20
x+24
x+28
x+32
x+36
10x+180=300
10x=120
x=12
3rd question = x+8 = 12+8 = 20
Answer D
Answer: (D) 20
Question: There are 85 doors marked with numbers 1 to 85. And there are 85 individuals marked 1 to 85.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with.
Now one at a time one randomly picked individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For e.g. individual marked with number 5 operates the doors marked with the following numbers: 5, 10, 15 ... 85.
If every individual in the group get one turn then how many doors are open at the end?
(A) 0
(B) 1
(C) 2
(D) 8
(E) 9
Rationale: Let us start with 1.
When 1 goes, all the doors are open since every number is a multiple of 1.
Also 1 will remain opened since 1 is not a multiple of any number.
Prime numbers can only be operated by people with prime numbers.
So 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59, 61,67,71,73,79,83 will be closed when people with respective numbers perform operations on them.
From the other numbers, only those numbers will remain opened on which even number of operations are performed including the operation performed by number 1.
This is possible only for perfect squares which are 4,9 ... 81.
So our numbers are 1,4,9,16,25,36,49,64,81.
Answer:- E
Answer: (E) 9
Question: A 12 month project had a total budget of $42,000. After eight months, the project had spent $23,700. At this point, how much was the project under budget?
(A) $4100
(B) $4300
(C) $4500
(D) $4700
(E) $4900
Rationale: Each month, the project should spend $42,000 / 12 = $3500.
In 8 months, the project should spend 8*$3500=$28,000.
The project is under budget by $28,000 - $23,700 = $4300.
The answer is B.
Answer: (B) $4300
Question: If M is the least positive integer that is divisible by every integer from 4 to 12 inclusive, then M/11 is =
(A)  40320
(B)  27720
(C)  20160
(D)  6720
(E)  2520
Rationale: The integer should be divisible by: 4, 5, 6, 7, 8, 9, 10, 11 and 12, that is 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 3*2^2. The least common multiple of these integers is the product of 11, 7, 5, 3^2 and 2^3. Then, M/11 is (11 * 7 * 5 * 3^2 * 2^3)/11 = 7*5*9*8 = 2520.
Answer: E.
Answer: (E)  2520
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 9 people all together .how many people can sit in a bus?
(A) 52
(B) 49
(C) 95
(D) 90
(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 = 9
Total People can seat= 81+9=90
ANSWER:D
Answer: (D) 90
Question: If n = 2×3×5×7×11×13×14, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even
(A) I only
(B) II only
(C) III only
(D) None of the above
(E) I and III
Rationale: Statement I: 600 = (2^3)*(3)*(5^2) this is true.
Statement 2 Since n is divisible by 19 so n+19 is also divisible by 19. So this is NOT true.
Statement 3: (n+4)/2 = n/2 + 2
So, ODD + 2 cannot be even.
So this is true.
Hence option (E).
Answer: (E) I and III
Question: The cost of carpeting a room 18 m long with a carpet 75 cm wide at 4.50 per metre is 810. The breadth of the room is:
(A) 7 m
(B) 7.5 m
(C) 8 m
(D) 8.5 m
(E) None of these
Rationale: Length of the carpet = TotalCost/Rate/m
= (8100⁄45)m = 180 m.
Area of the room = Area of the carpet
= (180 × 75⁄100) m2 = 135 m2
∴ Breadth of the room = AreaLength=135/18m
= 7.5 m
Answer B
Answer: (B) 7.5 m
Question: Average of prime numbers ranging 1 to 50 is?
(A) 23
(B) 22.86
(C) 21.86
(D) 21
(E) 21.95
Rationale: Explanation:
Average = (2+3+5+7+11+13+17+19+23+29+31+37+41+43+47)/15 = 328/15= 21.8666
Answer is C
Answer: (C) 21.86
Question: Find the compound ratio of (3:4), (4:5) and (1:2) is
(A) 1:2
(B) 2:3
(C) 3:10
(D) 4:10
(E) 3:2
Rationale: Required ratio = 3/4 * 4/5 * 1/2 = 3/10= 3:10
Answer is C
Answer: (C) 3:10
Question: A sum fetched a total simple interest of Rs. 6016.75 at the rate of 8 p.c.p.a. in 5 years. What is the sum?
(A) Rs. 16241.875
(B) Rs. 15041.85
(C) Rs. 15401.875
(D) Rs. 15041.875
(E) None of these
Rationale: Explanation:
Principal = Rs 100 x 6016.75/ 8 x 5
= Rs. 601675/40
= Rs. 15041.875
Answer: Option D
Answer: (D) Rs. 15041.875
Question: A woman can do a piece of work in 40 days. Man is 25% more efficient than Woman. In how many days a man can do the same piece of work?
(A) 32 days
(B) 33 days
(C) 35 days
(D) 54 days
(E) 62 days
Rationale: The ratio of the efficiencies of a woman and man = 100 : 125
= 4 : 5
The ratio of the days taken by woman and man to finish the work = 5 :4
Woman takes 32 days to finish the work.=> 5 parts = 40
The number of days taken by man to finish the work = 4 parts = 40/5x 4 = 32 days
A
Answer: (A) 32 days
Question: A train is 510 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 76 seconds
(B) 18 seconds
(C) 52 seconds
(D) 19 seconds
(E) 45 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 510+140 = 650 meter
Time = Distance/speed
= 650 * (2/25)
= 52 seconds
Answer: C
Answer: (C) 52 seconds
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
(A) 5/21
(B) 5/28
(C) 5/25
(D) 5/23
(E) 5/22
Rationale: Number of ways of (selecting at least two couples among five people selected)
As remaining person can be any one among three couples left.
Required probability
= (10 * 6)/252 = 5/21
Answer: A
Answer: (A) 5/21
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: A number will be divisible by 3 if sum of all the digits of the number is divisible by 3
Here the Possible sum of the two distinct digits can be 3, 6, 9 and 12 only in order to satisfy the given condition
If sum of Digits = 3, No. = 12, 21 --- 2 Cases
If sum of Digits = 6, No. = 15, 24, 42, 51 --- 4 Cases
If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases
If sum of Digits = 12, No. = 57, 75 --- 2 Cases
Total Cases = 2+4+6+2 = 14 cases
Answer: option E
Answer: (E) 14
Question: 2+3=8,
3+7=27,
4+5=32,
5+8=60,
6+7=72,
7+8=??
Solve it?
(A) 78
(B) 98
(C) 88
(D) 68
(E) 58
Rationale: B
98
2+3=2*[3+(2-1)]=8
3+7=3*[7+(3-1)]=27
4+5=4*[5+(4-1)]=32
5+8=5*[8+(5-1)]=60
6+7=6*[7+(6-1)]=72
therefore
7+8=7*[8+(7-1)]=98
x+y=x[y+(x-1)]=x^2+xy-x
Answer: (B) 98
Question: A train 110 m long is running with a speed of 80 km/hr. In what time will it pass a man who is running at 8 km/hr in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 4.5
(D) 8
(E) 9
Rationale: Speed of train relative to man = 80 + 8 = 88 km/hr.
= 88 * 5/18 = 220/9 m/sec.
Time taken to pass the men = 110 * 9/220 = 4.5 sec.
Answer: Option C
Answer: (C) 4.5
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
(A) 9
(B) 10
(C) 12
(D) 13
(E) 14
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: Of a certain group of 100 people, 40 graduated from High School K, 65 graduated from College Y, and 30 live in City Z. What is the greatest possible number of people in this group who did not graduate from High School K, did not graduate from College Y, and do not live in City Z ?
(A)  5
(B)  15
(C)  35
(D)  65
(E)  85
Rationale: 1. k+y+z+ky+yz+kz+kyz+ none=100. Fornoneto be maximum others have to be minimum
2. We know the underlined portions sum to 65 and that is the minimum value of others
3. Maximumnone= 100-65=35=C
Answer: (C)  35
Question: Find compound interest on $ 12000 at 15% per annum for 2 years 4 months, compounded annually.
(A) 4663.5
(B) 4203.5
(C) 4303.5
(D) 4403.5
(E) 4103.5
Rationale: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = $ [12000 X (1+­(15/100))2 X (1+((1/3)*15)/100)]
=$ [12000 * (23/20) * (23/20) * (21/20)]
= $ 16663.50	.
:. C.I. = Rs. (16663.50 - 12000) = $ 4663.50
Answer A.
Answer: (A) 4663.5
Question: Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 40% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?
(A) 2 to 6
(B) 1 to 3
(C) 3 to 5
(D) 3 to 4
(E) 3 to 2
Rationale: Correct Answer: A
Solution: A. We know that when Pam and Stanley were both working, the ratio was 2 boxes by Pam to 3 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 2 to 6. Answer A is correct.
Answer: (A) 2 to 6
Question: Let d > c > w > a. If c is twice as far from a as it is from d, and w is twice as far from c as it is from a, then (d - w)/(d - a) = ?
(A) 2/9
(B) 1/3
(C) 2/3
(D) 7/9
(E) 3/2
Rationale: Draw a number line and label with x and y. You would have:
Before calculating recognize it would be more effcient to express x or y in terms of the other. here 2x = 3y so x =3/2 y.
Now you can calculate d -w and d -a
d - w= x +2y = 7/2 y
d - a = x + 2x = 3x = 9/2y
Dividing both you get: 7/9
Answer D
Answer: (D) 7/9
Question: An article costs Rs. 600. What should be the marked price of an article so that after 10% discount, the trader makes 20% profit?
(A) Rs. 800
(B) Rs. 950
(C) Rs. 1100
(D) Rs. 1040
(E) None of these
Rationale: Explanation:
Cost price of article = Rs. 600
Profit % = 20%
Therefore,
selling price of article = 120% of C.P.
= (120 / 100) * 600 = Rs. 720
Marked price = ?
Discount % = 10%
S.P. = Rs. 720
90% of M.P. = S.P.
90/100 * M.P. = 720
M.P. = 720 * (100/90) = Rs. 800
ANSWER A
Answer: (A) Rs. 800
Question: The sum of three integers is 22. The largest integer is 3 times the middle integer, and the smallest integer is 13 less than the largest integer. What is the product of the three integers?
(A) 130
(B) 140
(C) 150
(D) 160
(E) 170
Rationale: Let x be the middle integer. Then the largest is 3x and the smallest is 3x - 13.
3x - 13 + x + 3x = 22
x = 5
The three integers are 2, 5, and 15.
The product is 2*5*15 = 150
The answer is C.
Answer: (C) 150
Question: In how many ways can 7 beads can be arranged to form a necklace?
(A) 360
(B) 780
(C) 23
(D) 10
(E) 89
Rationale: Number of arrangements possible
=12(7−1)!=12×6!=12×6×5×4×3×2×1=360
Answer is A
Answer: (A) 360
Question: A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?
(A) 22 lakhs
(B) 21 lakhs
(C) 28 lakhs
(D) 67 lakhs
(E) 18 lakhs
Rationale: Explanation:
Let Rs.x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (3,500,000 - x).
The elder daughter’s money earns interest for (21 - 16) = 5 years @ 10% p.a simple interest.
The younger daughter’s money earns interest for (21 - 8.5) = 12.5 years @ 10% p.a simple interest.
As the sum of money that each of the daughters get when they are 21 is the same,
Answer: B) 21 lakhs
Answer: (B) 21 lakhs
Question: The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 8400 for a computer table, then what was the cost price of the computer table?
(A) Rs. 5725
(B) Rs. 5275
(C) Rs. 6275
(D) Rs. 6720
(E) None of these
Rationale: CP = SP * (100/(100 + profit%))
= 8400(100/125) = Rs. 6720.
ANSWER:D
Answer: (D) Rs. 6720
Question: 1,235
1,253
1,325
.....
....
+5,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,5 exactly once in each integer. What is the sum of these 24 integers?
(A) 73,326
(B) 78,524
(C) 84,820
(D) 89,918
(E) 95,560
Rationale: In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.
Then the sum equals 6(1111)+6(2222)+6(3333)+6(5555) = 73,326
The answer is A.
Answer: (A) 73,326
Question: Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 8 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: if n =9
mark sold 1 box
and Ann sold 7 boxes
total 8 < 9
Answer:E
Answer: (E) 9
Question: When Q is divided by N, the quotient is R and the remainder is E. Which of the following expressions is equal to E?
(A) RN + Q
(B) RN - Q
(C) Q - RN
(D) QN - R
(E) Q/R
Rationale: Q/N = R + E/N
Q -RN = E
Amswer: C
Answer: (C) Q - RN
Question: A car starts from A for B travelling 20 km an hour.1 1/2 hours later another car starts from A and travelling at the rate of 30 km an hour reaches B 2 1/2 hours before the first car. Find the distance from A to B.
(A) 280 km
(B) 260km
(C) 240km
(D) 340km
(E) None of these
Rationale: Let the distance between A and B be x
The second car stars 1.5 hour later and reaches 2.5 hour early then first car
so the time difference is 4 hours.
Thus, x/20 - x/ 30 = 4
or, x = 240
ANSWER:C
Answer: (C) 240km
Question: Find the lowest common multiple of 24, 36 and 40.
(A) 120
(B) 240
(C) 360
(D) 480
(E) 530
Rationale: 2 | 24 - 36 - 40
--------------------
2 | 12 - 18 - 20
--------------------
2 | 6 - 9 - 10
-------------------
3 | 3 - 9 - 5
-------------------
| 1 - 3 - 5
L.C.M. = 2 x 2 x 2 x 3 x 3 x 5 = 360.
Answer: Option C
Answer: (C) 360
Question: Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines to gather must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time Q, in hours, that machine B must operate?
(A) 4
(B) 4 2/3
(C) 5 1/3
(D) 6
(E) 6 1/4
Rationale: Machine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time Q, in hours, that machine B must operate?
a) 4
b) 4 and 2/3
c) 5 and 1/3
d) 6
e) 6 and 1/4
To minimize the time that machine B must operate we must maximize the time machine A can operate, so make it operate 8 hours. In 8 hours machine A will produce 8*9,000=72,000 pencils, so 100,000-72,000=28,000 pencils are left to produce, which can be produced by machine B in 28,000/7,000=4 hours.
Answer: A.
Answer: (A) 4
Question: A 21 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 12
(B) 6
(C) 88
(D) 77
(E) 14
Rationale: 1: 2/5 = 5: 2
2/7 * 21 = 6
Answer: B
Answer: (B) 6
Question: Each of the 59 members in Peter's school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?
(A) 2
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Each of the 59 members in Peter's school class is required to sign up for a minimum of one and a maximum of three academic clubs. Total = G1 + G2 + G3 - (# In exactly 2) - 2*(# in 3 sets)
59 = 22+27+28 - (6) - 2x
so, # In 3 sets = 6=C
Answer: (C) 6
Question: A driver took a trip consisting of three segments at three different speeds. The driver drove a distance of (7D) at a speed of (2V), then a distance of (10D) at a speed of (3V), then a distance of D at a speed of (6V). In terms of D and V, what was the total time of the trip?
(A) 3D/V
(B) 4D/V
(C) 5D/V
(D) 6D/V
(E) 7D/V
Rationale: The total time of the trip was:
7D/2V + 10D/3V + D/6V =
42D/12V + 40D/12V + 2D/12V =
84D/12V = 7D/V
The answer is E.
Answer: (E) 7D/V
Question: A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 3
(B) 4
(C) 5
(D) 8
(E) 9
Rationale: Explanation:
50 + 25 = 75/15 = 5 (Remainder)
C
Answer: (C) 5
Question: The bankers discount of a certain sum of money is Rs. 576 and the true discount on the same sum for the same time is Rs. 480. The sum due is:
(A) 2880
(B) 2870
(C) 2860
(D) 2850
(E) 2840
Rationale: Sum = (B.D*T.D)/(B.D-T.D)
(576*480)/576-480;
2880
ANSWER:A
Answer: (A) 2880
Question: Q is a set of six distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: 2 + 3 + 5 + 7 + 11 + 13 = 41 (Discard as sum is ODD)
3 + 5 + 7 + 11 + 13 + 17 = 56 (Sum is even)
Least number = 3
B
Answer: (B) 3
Question: Can anyhow help me with an easy solution for this
2, 3, 9, 5, 6, 81, 6, 7, ?
(A) 256
(B) 221
(C) 121
(D) 144
(E) 169
Rationale: 2, 3, 9, 5, 6, 81, 6, 7, ?
2+73=5 and 5-2=3 and 3^2=9
5+6=11 and 11-2=9 and 9^2=81
6+7=13 and 13-2=11 and 11^2=121
ANSWER:C
Answer: (C) 121
Question: Can you deduce the pattern and find the next number in the series?
7, 15, 27, 99, __?
(A) 276
(B) 277
(C) 278
(D) 279
(E) None of these
Rationale: Solution:
277
Explanation:
7 = (1^1 + 2^1 + 3^1) +1
15 = (1^2 + 2^2 + 3^2) +1
37 = (1^3 + 2^3 + 3^3) +1
99 = (1^4 + 2^4 + 3^4) +1
Thus the next number will be
(1^5 + 2^5 + 3^5) +1 = 277
Answer B
Answer: (B) 277
Question: On the blueprint there are 4 line measurements A, B, C, and D. If A:B = .437/.762, B:C = .762/3, C:D = 3/.146, then what is the total measurement for line B:D?
(A) 3.937
(B) 1
(C) 5.219
(D) 20.547
(E) 20.548
Rationale: Solution
A : B = .437 : .762,
B : C = .762 : 3,
C : D = 3 : .146
âˆ´Aâˆ¶Bâˆ¶Câˆ¶D= .437 : .762 : 3 : .146.
Thus, B : D = .762 : .146
Correct Option C
Answer: (C) 5.219
Question: 3 events last together 240 days. Event A last as many seconds as event B in minutes, and event A last as many hours and event C in days. How long does event C last in days?
(A) 170 days
(B) 40 days
(C) 204 days
(D) 68 days
(E) 60 days
Rationale: Let c be C’s duration in days. If b is B’s duration in days, then B lasts 1440b minutes. If a is A’s duration in days, then A lasts 86,400a seconds. Thus,86,400a = 1440bSince A is 24a hours long,24a = cSince A, B and C last together 240 days, a + b + c = 240 days.The above system of 3 equations in 3 unknowns (a, b and c) can be solved as follows:c / 24 + 3600c / 1440 + c = 240 or60c + 3600c +1440c = 345,600 orc = 345,600 / 5100 = 68 daysAnswer = D
Answer: (D) 68 days
Question: In a box, there are 10 red, 6 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green ?
(A) 4/51
(B) 10/21
(C) 7/12
(D) 5/21
(E) 13/17
Rationale: Total number of balls = 10+6+5 = 21
E = event that the ball drawn is neither red nor green
= event that the ball drawn is green
n(E) = 5
P(E) = 5/21
Answer is D
Answer: (D) 5/21
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 6:8
(B) 6:2
(C) 6:5
(D) 6:9
(E) 6:6
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer: C
Answer: (C) 6:5
Question: While driving from A-ville to B-town, Harriet drove at a constant speed of 105 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 145 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?
(A) 138
(B) 148
(C) 150
(D) 162
(E) 174
Rationale: 5hr = 300min.
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.
Now let plug in ans. D or E and verify which one give same distance on each leg.
E. t= 174min
* leg A-B ---> d = 105.174/60 = 18270/60
* leg B-A ----> d = 145*126/60 = 18270/60
so the correct ans. isE
Answer: (E) 174
Question: The average of five numbers is 27. if one number is excluded the average become 25. the excluded number is :
(A) 25
(B) 27
(C) 30
(D) 35
(E) 37
Rationale: Solution
Excluded number = (27 × 5) - (25 × 4) = 135 - 100 =35 . Answer D
Answer: (D) 35
Question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 19 1/7 days
(B) 16 1/7 days
(C) 14 1/7 days
(D) 17 1/7 days
(E) 13 1/7 days
Rationale: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
ANSWER:D
Answer: (D) 17 1/7 days
Question: The ages of two persons differ by 16 years. If 6 years agao, the elder one be 3 times as old as the younger one, find their present ages.
(A) 20 years.
(B) 30 years.
(C) 40 years.
(D) 50 years.
(E) 60 years.
Rationale: Sol.
Let the age of the younger person be x years.
Then, age of the elder perosn = (x + 16) years.
∴ 3(x - 6) = (x + 16 - 6) ⇔ 3x - 18 = x + 10
⇔ 2x = 28 ⇔ x = 14
Hence, their present ages are 14 years and 30 years.
Answer B
Answer: (B) 30 years.
Question: Renu can do a piece of work in 8 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone?
(A) 4.8
(B) 1.2
(C) 4.4
(D) 4.6
(E) 4.7
Rationale: Renuâ€™s one dayâ€™s work = 1/8
Sumaâ€™s one dayâ€™s work = 1/3 - 1/8 = 5/24
Suma can do it alone in 4.8 days.
ANSWER:A
Answer: (A) 4.8
Question: Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^2.
(A) 29
(B) 27
(C) 28
(D) 24
(E) 21
Rationale: (4)^11x (7)^5 x (11)^2 = (2 x 2)^11 x (7)^5 x (11)^2 = 2^11 x 2^11 x7^5x 11^2 = 2^22 x 7^5 x11^2
Total number of prime factors = (22 + 5 + 2) = 29.
Answer is A.
Answer: (A) 29
Question: Two sides of a triangle have lengths x and t and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to t ?
(A) a) 2 : 3
(B) b) 3 : 4
(C) c) 4 : 3
(D) d) 3 : 2
(E) e) 2 : 1
Rationale: Ahhhh....my bad. Thank you, you're correct. 8x = 6t --> x/t = 3/4.
Actually B is the right answer.
Answer: (B) b) 3 : 4
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
(A) 2777
(B) 2888
(C) 8400
(D) 2882
(E) 2781
Rationale: Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23 = Rs. 8400.
Answer: C
Answer: (C) 8400
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 15 minutes. The waste pipe can empty the full cistern in?
(A) 6
(B) 8
(C) 10
(D) 9
(E) 2
Rationale: 1/10 + 1/15 - 1/x = 1/15
x = 10
Answer:C
Answer: (C) 10
Question: If the radius of a circle is decreased 40%, what happens to the area?
(A) 10% decrease
(B) 20% decrease
(C) 36% decrease
(D) 40% decrease
(E) 64% decrease
Rationale: Area of Square = Pi* radius^2
New Radius = 0.6 * old radius
so new area = (0.6)^2 old area => 4/25 of old area => 36% old area
Ans : E
Answer: (E) 64% decrease