mathewhe/aqua_rat huggingface dataset:
Question: Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?
(A) 60
(B) 180
(C) 240
(D) 360
(E) 720
Rationale: F is in first position from the right, then the rest 5 positions can be filled in 5! ways=120
If F is in Second position; then the first position can be filled in 4 ways, and the rest 4 positions in 4! ways; i.e. 24*4=96
If F is in Third position; then the first and second position can be filled in 4 and 3 ways, and the rest 3 positions in 3! ways; i.e. 4*3*3!=72
If F is in Fourth position; then the first, second and the third position can be filled in 4, 3, and 2 ways ways, and the rest 2 positions in 2! ways; i.e. 4*3*2*2!=48
If F is in Fifth position; then the first, second third and the fourth position can be filled in 4, 3, 2 and 1 way, and the rest 1 positions in 1! ways; i.e. 4!=24
Hence, answer should be 360. answer D
Answer: (D) 360
Question: If the first day of a year (other than leap year) was Tuesday, then which was the last day of that year?
(A) Saturday
(B) Friday
(C) Tuesday
(D) Monday
(E) None of these
Rationale: Explanation :
Given that first day of a normal year was Tuesday
Odd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Tuesday+ 1 Odd day) = Wednesday
Therefore, last day of the mentioned year = Tuesday. Answer : Option C
Answer: (C) Tuesday
Question: If f(x)= 5x^2- 2x+6 and g(y)= 3y-6, then g(f(x))
(A) 82x^2-9x+38
(B) 15x^2-6x+12
(C) 58x^2-4x+58
(D) 87x^2-5x+96
(E) 98x^2-7x+94
Rationale: g(f(x))=3(5x^2-2x+6)-6
=15x^2-6x+18-6
=15x^2-6x+12
the answer is B
Answer: (B) 15x^2-6x+12
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
(A) 75000
(B) 80000
(C) 90000
(D) 67800
(E) 50000
Rationale: B
80,000.
The distance traveled by each tyre:
4/5 * 1, 00, 000km = 80,000 km.
Answer: (B) 80000
Question: If x/y = 0.3, then (2x - y)/(2x + y) = ?
(A) 0.25
(B) 0.5
(C) 0.4
(D) 0.45
(E) 0.34
Rationale: Explanation:
x = 0.3y
Then, (y - 2x)/(y + 2x)
= y - 2(0.3y)/y + 2(0.3y)
= y - 0.6y/y + 0.6y
= 0.4y/1.6y
= 0.4/1.6 = 0.25
Answer: Option A
Answer: (A) 0.25
Question: Suppose you want to buy three loaves of bread that cost $1.50 each
and a jar of peanut butter that costs $4. A jar of jelly is $2.75, but you
don’t need any jelly. You have $10. How much money will you have left
over?
(A) $1.50
(B) $2.50
(C) $3.50
(D) $4.50
(E) $5.50
Rationale: The jelly is extra information. 10.00 – 3 x 1.50 – 4.00 =
10.00 – 4.50 – 4.00 = 1.50.
You have $1.50 left.
correct answer A
Answer: (A) $1.50
Question: The side of a rhombus is 28 m and length of one of its diagonals is 12 m. The area of the rhombus is?
(A) 326.2
(B) 324.2
(C) 328.2
(D) 338.2
(E) 328.9
Rationale: area of the rhombus = 1/2 * p * √4(a)2 - (p)2
a= 28 ; p = 12
A=1/2 * 12 *√4(28)2 - (12)2
=1/2 * 12 *√3136 - 144
=1/2 * 12 *√2992
A =328.2
Answer : C
Answer: (C) 328.2
Question: From the set of numbers x, y, t, z and w, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc and (x,y)=(y,x)
(A) 10
(B) 14
(C) 15
(D) 16
(E) 30
Rationale: There are 4 letter without t: x, y, z, and w, so:
C14+C24+C34+C44=4+6+4+1=15
Any letter (x, y, z, w) can be included or not. So, we have 2^4 combinations - 1 empty combination = 15 combinations
Answer: C
Answer: (C) 15
Question: A number is four less than six times the other number. If the sum of both the number is 38, what are the numbers?
(A) 6,32
(B) 7,31
(C) 5,33
(D) 4,34
(E) None of the above
Rationale: that numbers are x,6x-4
so sum =x+6x-4=38
7x=42 ==> x=6
another no is 32
answer is 6, 32
ANSWER:A
Answer: (A) 6,32
Question: How many digits are in (8×10^8)(10×10^10)?
(A) 20
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: The question simplfies to (8×10^8)(10^11)
=> 8*10^19
=> Will contain 19 zeros +1 digit 8
=>20
Ans A
Answer: (A) 20
Question: In a 200 meters race A beats B by 35 m or 7 seconds.A’s time over the course is :
(A) 40 sec
(B) 47 sec
(C) 33 sec
(D) 35 sec
(E) None of these
Rationale: Solution
B runs 35 m in 7 sec.
∴ B covers 200 m in (7/35x200) =40 sec
B’s time over the course = 40 sec.
∴ A’s time over the course = (40-7)sec =33sec
Answer C
Answer: (C) 33 sec
Question: John makes $40 a week from his job. He earns a raise and now makes $80 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 17.9%
(D) 18.12%
(E) 100%
Rationale: Increase = (40/40)*100 = (1)*100 = 100%.
E
Answer: (E) 100%
Question: In a theatre all rows have same no. Of . One family buys 10 tickets of first two row. 3 members want to sit in first row and 2 in second row. In how many ways they can be seated.
(A) 5400
(B) 5500
(C) 5600
(D) 5700
(E) 5800
Rationale: 10c3x10c2= 5400
ANSWER:A
Answer: (A) 5400
Question: If x = y^2, and x and y are positive integers, which of the following could be the value of x?
(A) 24,336
(B) 36,847
(C) 42,007
(D) 49,003
(E) 64,643
Rationale: A square of an integer can have units digit as 0, 1, 4, 5, 6, 9.
B, C, D and E do not have the units digit as 0, 1, 4, 5, 6 or 9. Only option A has the units digit as 6.
Answer: A
Answer: (A) 24,336
Question: The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 44. What is a possible value for the mean of the distribution?
(A) 46
(B) 47
(C) 48
(D) 49
(E) 51
Rationale: The standard deviation ({SD}) = 2;
3 standard deviations below the mean is greater than 44:
{Mean} - 3*{SD} > 44;
{Mean} - 6 > 44;
{Mean} > 50.
Answer: E.
Answer: (E) 51
Question: The cost per unit of electricity during a 4 year period is as follows:
Year 1, $0.5 per unit;
Year 2, $1.0 per unit;
Year 3, $1.5 per unit;
Year 4, $2 per unit.
If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?
(A) $1.96
(B) $0.96
(C) $1.56
(D) $1.46
(E) $1.36
Rationale: Let money spent each year = $6
Units bought first year = 12
Units bought second year = 6
Units bought third year = 4
Units bought fourth year = 3
Total number of units = 25
Total money spent = 6*4 = 24
Average = 24/25 = 0.96
Answer : B
Answer: (B) $0.96
Question: Divide $600 among A,B in the ratio 1:3. How many $ that A get?
(A) $50
(B) $500
(C) $150
(D) $250
(E) $600
Rationale: Sum of ratio terms = 1+3= 4
A = 600*1/4 = $150
Answer is C
Answer: (C) $150
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 two years back was?
(A) 17 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 2 years back (19 - 2) = 17 years.
A
Answer: (A) 17 years
Question: What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142
(A) 23
(B) 25
(C) 46
(D) 49
(E) 50
Rationale: (C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30 + 16 = 46 .
Answer: (C) 46
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 150
(B) 200
(C) 130
(D) 100
(E) 250
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
ANSWER D
Answer: (D) 100
Question: What is the tens digit of 36^10?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 36^10 = 6^20
If you type powers of six they end in
6
36
16
96
76
56
the pattern is 3-->1-->9-->7-->5 so for 36 we start with 3-->9-->5-->1-->7 and repeat.
36^10 will come at 7.
Answer D.
Answer: (D) 7
Question: The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
(A) 30 pi m^2
(B) 40 pi m^2
(C) 60 pi m^2
(D) 80 pi m^2
(E) 100 pi m^2
Rationale: l = 10 m
h = 8 m
r = root(i^2-h^2) = root(10^2 - 8^2) = 6 m
curved surface area = pi ri=60 pi m^2
ANSWER C
Answer: (C) 60 pi m^2
Question: a and b are two numbers selected randomly from 1,2,3.... 25 what is the probability of a and b are not equal.
(A) 24/28
(B) 24/25
(C) 24/209
(D) 22/43
(E) 24/19
Rationale: Explanation:
Total outcomes = 25 × 25 = 625
Probability of getting a and b are equal= 25 [ ∴ (1,1),(2,2),(3,3).....(25,25)]
Probability of a and b or not equal = 1−256251−25625 = 600625600625 = 24/25
Answer: B
Answer: (B) 24/25
Question: A batsman scored 160 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets.
(A) 64%
(B) 66%
(C) 60%
(D) 68%
(E) 70%
Rationale: Explanation:
Number of runs made by running = 160 - (3 x 4 + 8 x 6)
= 160 - (60)
= 100
Now, we need to calculate 100 is what percent of 160.
=> 100/160 * 100 = 68
Option D
Answer: (D) 68%
Question: A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is
(A) 2451
(B) 1200
(C) 1234
(D) 5874
(E) 4561
Rationale: Explanation:
2(15 + 12) x h = 2(15 x 12)
h =	180/27m =20/3m.
Volume =	15 x 12 x	20/3	m	= 1200 m^3.
Ans: B
Answer: (B) 1200
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
(A) 22
(B) 15
(C) 66
(D) 88
(E) 19
Rationale: Explanation:
Dividend on Rs. 20 = Rs. (9/100)x 20 = Rs.9/5.
Rs. 12 is an income on Rs. 100.
Rs.9/5 is an income on Rs.[ (100/12) x (9/5)] = Rs. 15.
Answer: B) 15
Answer: (B) 15
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 44
(B) 87
(C) 16
(D) 88
(E) 99
Rationale: 10 * 15 + 36 – 26
= 160/10
= 16
Answer:C
Answer: (C) 16
Question: 12 persons can complete the work in 18 days. After working for 6 days, 4 more persons added to complete the work fast.In how many days they will complete the work?
(A) 10
(B) 15
(C) 17
(D) 5
(E) 9
Rationale: Total work=12*18 =216 units.
After 6 days, work finished=6*12=72 units.
Remaining units=216-72=144 units.
Remaining days=144/(2+4)=9 days
The option is E
Answer: (E) 9
Question: A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is:
(A) 5 12/8 %
(B) 5 15/12 %
(C) 5 15/8 %
(D) 6 12/17 %
(E) 5 15/17 %
Rationale: C.P. of 1st transistor = Rs.	(100/120 x 840 )= Rs. 700
C.P. of 2nd transistor = Rs.	(100/96 x 960)	= Rs. 1000
So, total C.P. = Rs. (700 + 1000) = Rs. 1700.
Total S.P. = Rs. (840 + 960) = Rs. 1800.
Gain % =	(100/1700 x 100)%=5 15/17 %
Answer: E
Answer: (E) 5 15/17 %
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?
(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000
Rationale: SI for 1st year = 550/2=275
275+275+SI on (275)=605==> SI on 275=55==>
SI on 275 = 275*R*1/100=55
R=20%
Now using SI for 2 years on T/2 of the money
(T/2)*20*2/100=550
T=550*5= 2750
ANSWER:A
Answer: (A) $2,750
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer)
(A) 4299
(B) 4228
(C) 4287
(D) 4266
(E) 4227
Rationale: CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73
= Rs.4266
Answer: D
Answer: (D) 4266
Question: A local bank that has 23 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 23 codes?
(A) 3
(B) 4
(C) 6
(D) 5
(E) 7
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Add one more integer: 5
55, 15, 51, 25, 52, 35, 53,54,45 = 9 Codes
Total = 25 Codes. Enough.
Answer: D
Answer: (D) 5
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 35000. What was Simran's share in the profit?
(A) Rs. 9423
(B) Rs. 10,250
(C) Rs. 12,500
(D) Rs. 15,000
(E) None of these
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 35000 * 3/7 = Rs. 15000
ANSWER:D
Answer: (D) Rs. 15,000
Question: What is the least number of squares tiles required to pave the floor of a room 2 m 25 cm long and 1 m 35 cm broad?
(A) 15
(B) 20
(C) 40
(D) 44
(E) 48
Rationale: Length of largest tile = H.C.F. of 225 cm and 135 cm = 45 cm.
Area of each tile = (45 x 45) cm2.
Required number of tiles =225 x 135/(45^2)= 15.
ANSWER:A
Answer: (A) 15
Question: The annual interest rate earned by an investment increased by 6 percent from last year to this year. If the annual interest rate earned by the investment this year was 15.90 percent, what was the annual interest rate last year?
(A) 20%
(B) 18%
(C) 16%
(D) 25%
(E) 15%
Rationale: let i = interest rate
i(this year) = i(last year) + 0.06i(last year) = 1.06i(last year)
15.90 = 1.06 x i(last year)
i(last year) = 15.90/1.06 = 1590/106 = 15%
Answer : E
Answer: (E) 15%
Question: X can finish a work in 20 days. Y can finish the same work in 15 days. Yworked for 9 days and left the job. how many days does X alone need to finish the remaining work?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Work done by X in 1 day = 1/20
Work done by Y in 1 day = 1/15
Work done by Y in 9 days = 9/15 = 3/5
Remaining work = 1 – 3/5 = 2/5
Number of days in which X can finish the remaining work = (2/5) / (1/20) = 8
D
Answer: (D) 8
Question: Walking with 4/5 of my usual speed, I arrive at the bus stop 7 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: Let t = usual time = distance / usual speed
t + 7 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4
t = 28
The answer is E.
Answer: (E) 28
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 170. If the ratio of his marks in English and Maths is 1:4, find his marks in Science?
(A) 17
(B) 77
(C) 66
(D) 55
(E) 31
Rationale: S:E = 1:3
E:M = 1:4
------------
S:E:M = 1:4:12
1/17 * 170 = 17
Answer: A
Answer: (A) 17
Question: Two trains are moving in the same direction at 90 kmph and 36 kmph. The faster train crosses a man in the slower train in 29 seconds. Find the length of the faster train?
(A) 425
(B) 435
(C) 445
(D) 455
(E) 465
Rationale: Relative speed = (90 - 36) * 5/18 = 3 * 5
= 15 mps.
Distance covered in 29 sec
= 29 * 15
= 435 m.
The length of the faster train
= 435 m.
Answer:B
Answer: (B) 435
Question: A train running at the speed of 60 km/hr crosses a pole in 3 seconds. Find the length of the train.
(A) 150 m
(B) 50 m
(C) 75 m
(D) 135 m
(E) 60 m
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 3 = 50 meter
ANSWER: B
Answer: (B) 50 m
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
(A) 3977
(B) 2887
(C) 3972
(D) 26990
(E) 27012
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
Answer: C
Answer: (C) 3972
Question: A man can row downstream at 16 kmph and upstream at 12 kmph. Find the speed of the man in still water .
(A) 14
(B) 13
(C) 12
(D) 16
(E) 15
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 16 --- (1)
and x - y = 12 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 2.
Answer:A
Answer: (A) 14
Question: The price of a TV was increased by 30 percent. The new price was then increased by 20 percent. A single increase of what percent is equivalent to these two successive increases?
(A) 50%
(B) 60%
(C) 65%
(D) 56%
(E) 45%
Rationale: consider base price - $100
25% increase = 1.30*100 = $130
another 20% increase on new price = 1.2* 130 = $156
so final price of radio - $156
therefore a 56% increase
correct option - D
Answer: (D) 56%
Question: If a = (1/2)b and c = 3a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?
(A) 2a
(B) 3a
(C) 4a
(D) 5a
(E) a/2
Rationale: a = (1/2)b --> b=2a.
The mean = (a + b + c)/3 = (a + 2a + 3a)/3 = 2a.
Answer is A
Answer: (A) 2a
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
(A) 36
(B) 39
(C) 42
(D) 45
(E) None of the above
Rationale: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
∴ 16(x – 3) + 87 = 17x or x = (87 – 48) = 39.
Answer B
Answer: (B) 39
Question: If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x?
(A) 12,947
(B) 13,872
(C) 14,323
(D) 15,568
(E) 16,641
Rationale: The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.
The answer is E.
Answer: (E) 16,641
Question: Two persons C & D started traveling from A and B which are 300 km apart, towards B and A
respectively at 1.00 p.m. C travels at a constant speed of 30 kmph whereas D doubles his speed every
hour. If D reaches A in 4 5/8 hours, at what time did C and D meet each other ?
(A) 4:30 p.m.
(B) 4:40 p.m
(C) 5:00 p.m
(D) 5:10 p.m.
(E) 6:10 p.m.
Rationale: Let speed of D in first hour = x
D’s speed = x+ 2x+ 4x+ 8x+ 16x*(5/8) = 25x
Given 25x=300 :. X = 12
At the end of four hours C traveled 120 (30 *4) kmph and D traveled 12 + 24+ 48 +96 = 180kmph
:. They meet each other after 4 hours ie at 5: p.m.
Answer : C
Answer: (C) 5:00 p.m
Question: The ration of the number of boys and girls in a college is 7:8. If the percentage is increase in the number of boys and girls be 20% and 10% respectively. What will be the new ration?
(A) 5:7
(B) 15:21
(C) 21:22
(D) 13:17
(E) 23:42
Rationale: Let the number of boys and girls be 7x and 8x
their increased number is 120% of 7x and 110% of 8x
7x*120/100 and 8x*110/100
42x/5 and 44x/5
Required ratio = 42x/5 : 44x/5 = 21:22
Answer is C
Answer: (C) 21:22
Question: In a contest, a bowl contains 14 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
(A) 1/14
(B) 1/7
(C) 13/140
(D) 2/21
(E) 7/182
Rationale: P(not winning) = 13/14*12/13 = 6/7
P(winning) = 1 - 6/7 = 1/7
The answer is B.
Answer: (B) 1/7
Question: 12,?,68,129,220,347,516
(A) 129
(B) 220
(C) 347
(D) 31
(E) 520
Rationale: 2*2*2 + 4 = 12
4*4*4 + 4 = 68
5*5*5 + 4 = 129
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
8 *8 *8 + 4 = 516.
3*3*3 +4 = 31
ANSWER : D
Answer: (D) 31
Question: If 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
(A) 55
(B) 42
(C) 43
(D) 44
(E) 45
Rationale: n(n-1)/2 =11*10/2
=55
ANSWER:A
Answer: (A) 55
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) 647
(B) 738
(C) 654
(D) 847
(E) 976
Rationale: S.I. for 1 year = Rs. (854 - 825) = Rs. 29.
S.I. for 3 years = Rs.(29 x 3) = Rs. 87.
Principal = Rs. (825 - 87) = Rs. 738
Answer:B
Answer: (B) 738
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:6
(B) 3:4
(C) 3:7
(D) 3:9
(E) 3:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B
=6000 : 8000 => 3:4
Answer: B
Answer: (B) 3:4
Question: 150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?
(A) 90days
(B) 60days
(C) 67days
(D) 70days
(E) 66days
Rationale: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = 7x/30 kg.
Quantity consumed by 70 men in x days = (7x/30)(70)kg
(7x/30)(70) = 980
x = (980 * 30)/490 => x = 60 days
Answer & Answer: B
Answer: (B) 60days
Question: A box contains 3 red balls and 3 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
(A) 1/4
(B) 1/2
(C) 1/2
(D) 2
(E) 2/3
Rationale: My complicated version of your simple approach
Let the 3 black balls be BBB and 3 Red Balls be RRR
They can be arranged in 8 slots _ _ _ _ _ _ _ _
in (6!)/ (3!x3!)
If the fourth slot is Black ball then the arrangement will be to fill
_ _ _ B _ _ _ _
we have 5 slots and 2 Black (BB) and 3 Red (RRR)
They can be arranged in (5!)/ (2!x3!)
Hence required probability = [(6!)/ (3!x3!)]/[(5!)/ (2!x3!)]
=2
D
Answer: (D) 2
Question: A, B and C rents a pasture for Rs.730. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 199
(C) 676
(D) 156
(E) 227
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 730= 227
Answer: E
Answer: (E) 227
Question: Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team T. If team A's average speed was 5 mph greater than team T's, what was team T's average mph?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.
Say Team T's speed was s. Then Team T's time is 300/s.
Team A's speed was then s+5, and Team A's time was then 300/(s+5).
We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team T. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer D, you find the time for Team T is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, D is correct.
Answer: (D) 20
Question: The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x � 16
(x � 6) = 3 (x-16-6)
=> x � 6 = 3x � 66
=> 2x = 60
=> x = 60/2 = 30
Answer: Option D
Answer: (D) 30
Question: What is the greatest positive integer n such that 3^n is a factor of 36^50?
(A) 100
(B) 200
(C) 300
(D) 600
(E) 900
Rationale: 36 = 3^2 * 2^2.
36^50 = 3^100 * 2^100
The answer is A.
Answer: (A) 100