mathewhe/aqua_rat huggingface dataset:
Question: 40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
(A) 12
(B) 61
(C) 17
(D) 90
(E) 15
Rationale: Given, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 40% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/40 = 60
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (60 + 120)/2 = 90.
Answer: D
Answer: (D) 90
Question: A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? (Its a Previously asked on SSC 2012 exam) (*without a train question it is impossible to conduct an exam, I think you got, what I mean)
(A) 40.4 sec
(B) 50.4 sec
(C) 40.5 sec
(D) 50.5 sec
(E) 52.0 sec
Rationale: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 770 m
Time = Distance / Speed
= 770 x 18 / (5 x 55)
= 50.4 sec
Answer: OPTION B
Answer: (B) 50.4 sec
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps	4	:	3 :: 8 : x
Days 1	:	2
Therefore, 4 x 1 x x = 3 x 2 x 8
=> x =(3 x 2 x 8) / (4)
x = 12.
Correct answer is D
Answer: (D) 12
Question: The sum of number of boys and girls in a school is 1150. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?
(A) 50
(B) 40
(C) 60
(D) 92
(E) 70
Rationale: We have x+x% of 1150 = 1150
x + x/100 * 1150 = 1150
25/2 * x = 1150
x = 1150*2/25 = 92
Answer is D
Answer: (D) 92
Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 10, what is the sum of the first 15 terms of the progression?
(A) 65
(B) 75
(C) 60
(D) 55
(E) 50
Rationale: 4th term + 12th term = 10
i.e., (a+3d)+(a+11d) = 10
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 10 --------------- From (1)
=75
Answer : B
Answer: (B) 75
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
(A) 4000
(B) 345
(C) 5673
(D) 4530
(E) 4566
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
Answer: Option D
Answer: (D) 4530
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
(A) 19828.83
(B) 19828.8
(C) 19828.82
(D) 19828.89
(E) 19828.81
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80.Answer:B
Answer: (B) 19828.8
Question: What amount does an investor receive if the investor invests $5000 at 10% p.a. compound interest for two years, compounding done annually?
(A) $5850
(B) $5950
(C) $6050
(D) $6150
(E) $6250
Rationale: A = (1 + R/100)^n * P
(1.1)^2 * 5000 = 1.21 * 5000 = 6050
The answer is C.
Answer: (C) $6050
Question: If shares of two persons in profits are Rs.600 and Rs.1000 then ratio of their capitals is
(A) 3:5
(B) 2:3
(C) 4:3
(D) 1:3
(E) 1:2
Rationale: profit=time*capital
so 600:1000=3:5
ANSWER:A
Answer: (A) 3:5
Question: What is the median from the below series
32, 36, 34, 29, 28, 37, and 39
(A) 29
(B) 34
(C) 37
(D) 39
(E) 32
Rationale: Ordering the data from least to greatest, we get:
28, 29, 32, 34, 36, 37, 39
The median number was 34. (three numbers were higher than 34	and three were lower.)
B
Answer: (B) 34
Question: A cycle is bought for Rs.670 and sold for Rs.880, find the gain percent?
(A) 31%
(B) 35%
(C) 54%
(D) 38%
(E) 80%
Rationale: Explanation:
670 ---- 210
100 ---- ? => 31%
Answer: A
Answer: (A) 31%
Question: How many days per calendar year is the month a factor of the day
(A) 0
(B) 1
(C) 59
(D) 90
(E) 101
Rationale: Solution: 1
All 31 days in January, because 1 is a factor of all integers
14 of the 28 days in February (because every other day is divisible by 2)
10 of the 31 days in March (the multiples of 3 between 3 and 30)
7 days in April (the multiples of 4 between 4 and 28)
6 days in May (the multiples of 5 between 5 and 30)
5 days in June (the multiples of 6 between 6 and 30)
4 days in July (the multiples of 7 between 7 and 28)
3 days in August (the multiples of 8 between 8 and 24… so, so close if only the month were 32 days long!)
3 days in September (9th, 18th, 27th)
3 days in October (10th, 20th,30th)
2 days in November (11th, 22nd)
2 days in December (12th, 24th)
And there you have it! As you can see, as you move through the months, your job starts to get easier as you pick up on the patterns and are able to reuse some of your previous insights… This is a very valuable skill to remember on test day!
B
Answer: (B) 1
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 15%, then the cost price of the article is:
(A) 487
(B) 277
(C) 222
(D) 297
(E) 111
Rationale: Explanation:
120% of S.P. = 616
S.P. = (616 * 100)/120 = Rs. 560
C.P = (100 * 560)/115 = Rs. 487
Answer:A
Answer: (A) 487
Question: What number is that, which is to 12 increased by three times the number, as 2 to 9 ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Let x = the number sought.
Then x/12 + x + 12 = 64.
And x - 624/13 = 48.
Answer: (A) 6
Question: One hour after Yolanda started walking from X to Y, a distance of 52 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?
(A) 28
(B) 23
(C) 22
(D) 21
(E) 19.5
Rationale: When B started walking Y already has covered 3 miles out of 52, hence the distance at that time between them was 52-3=49 miles.
Combined rate of B and Y was 3+4=7 miles per hour, hence they would meet each other in 49/7=7 hours. In 6 hours B walked 7*4=28 miles.
Answer: A.
Answer: (A) 28
Question: Amanda has had 3 pay cuts in her salary in the past 6 months. If the first pay cut was 10%, the second pay cut was 10% and the third was 10%. What will be the percentage decrease, if the salary is decreased in a single shot?
(A) 27.1%
(B) 29.1%
(C) 21.1%
(D) 23.1%
(E) 25.1%
Rationale: Let Rs.100 be initial salary.
Salary After 1st decrease, 10% = 90
Salary After 2nd decrease, 10% = 81 i.e. reduced by 19 percent of 90
Salary After 3rd decrease, 10% = 72.9 i.e. reduced by 10 percent of 81
So if its decreased in single shot =
i = ( ( b - a ) /b ) * 100
=27.1%
ANSWER:A
Answer: (A) 27.1%
Question: The tax on a commodity is diminished by 10% and its consumption increased by 20%. The effect on revenue is?
(A) 2% decrease
(B) 8% increase
(C) 9% decrease
(D) 3% decrease
(E) 2% decrease
Rationale: 100 * 100 = 10000
90 * 120 = 10800
-----------
10000-----------800
100-----------? => 8% increase
Answer: B
Answer: (B) 8% increase
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Five years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
(A) A)24
(B) B)89
(C) C)40
(D) D)56
(E) E)45
Rationale: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then,	(5x + 5/4x + 5)=11/9
9(5x + 5) = 11(4x + 5)
45x + 45 = 44x + 55
45x - 44x = 55 - 45
x = 10.
Anand's present age = 4x = 40 years.
Answer:C
Answer: (C) C)40
Question: Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 5 meters per second and Jerry is running 50% slower, how much time will it take them to meet if the initial distance between the two is 200 meters and Tom started running 40 seconds before Jerry did?
(A) 40 sec
(B) 35 sec
(C) 1 mnt
(D) 52 sec
(E) 30 sec
Rationale: Tom is running alone for 40 seconds.
So he will cover a distance of 40*5 = 200 m in 40 seconds.
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side
answer is A
Answer: (A) 40 sec
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $48. If $1500 is the total amount invested, how much is invested at 8 percent?
(A) a. $280
(B) b. $566.67
(C) c. $892
(D) d. $1108
(E) e. $1200
Rationale: 2 equations with 2 unknowns
10x / 100 - 8y / 100 = 48
and
x + y = 1500
Solving these 2 equations, x = 933.33 and y = 566.67
Answer B.
Answer: (B) b. $566.67
Question: Jack, Jill, and Sandy each have one try to make a basket from half court. If their individual probabilities of making the basket are 1/6, 1/7, and 1/8 respectively, what is the probability that Jack and Jill will make a basket but Sandy will miss?
(A) 1/8
(B) 1/16
(C) 1/48
(D) 1/96
(E) 1/168
Rationale: The probability that Jack and Jill will make a basket but Sandy will miss is 1/6*1/7*7/8=1/48.
The answer is C.
Answer: (C) 1/48
Question: 6000−(105÷21.0)=?
(A) 6100
(B) 5100
(C) 550
(D) 598
(E) 5995
Rationale: Explanation:
=6000−(105/21)
=6000−5=5995
Option E
Answer: (E) 5995
Question: If 16x = 64^y, which of the following expresses x in terms of y?
(A) 4^(3y-2)
(B) 4^(y-1)
(C) 4^(2y-1)
(D) 4^(2y-3)
(E) 4^y
Rationale: By exponential simplification. 16 = 4^2 and 64=4^3 therefore (4^2)x=(4^3)^y gives x=(4^3y)/(4^2) further simplified to x=(4^3y)(4^-2) which gives x=4^(3y-2) Because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: A
Answer: (A) 4^(3y-2)
Question: A jar has 6 green 4 red and 2 blue marbles what is the probability of drawing 2 marbles randomly and they will be of different colors
(A) 1/4
(B) 1/2
(C) 2/3
(D) 7/9
(E) 8/15
Rationale: 1G and 1R
OR
1G and 1B
OR
1R and 1B
C61∗C41+C61∗C21+C41∗C21C122C16∗C14+C16∗C12+C14∗C12C212
24+12+866=4466=2324+12+866=4466=23
Ans: "C"
Answer: (C) 2/3
Question: If {p} denote the remainder when 3p is divided by 2 then which of the following is equal to 1 for all positive integers p?
I. {2p+1}
II. {2p}+1
III. 2{p+1}
(A) I only
(B) II only
(C) I and II
(D) III only
(E) II and III
Rationale: C - I and II
3p/2 = 0 or 1
I just substituted 1 in the equations and solved.
Answer: (C) I and II
Question: At a certain organisation, the number of male members went up by 12% in the year 2001 from year 2000, and the number of females members went down by 5% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000?
(A) 1:2
(B) 1:3
(C) 2:3
(D) 3:2
(E) 4:7
Rationale: men increase by 12% ==> 1.12M = males in 2001
women decrease by 5% ==> 0.95F = women in 2001
total employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001
Obviously
(males in 2001) + (females in 2001) = total number of employees in 2001
1.12M + 0.95F = 1.012*(M + F)
1.12M + 0.95F = 1.012M + 1.012F
1.12M - 1.012M = 1.012F - 0.95F
0.108M = 0.062F
M/F = (0.062)/(0.108) = 62/108 = 4/7
Answer =(E)
Answer: (E) 4:7
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 240
(C) 250
(D) 260
(E) 279
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: Option A
Answer: (A) 230
Question: A certain list has an average of 6 and a standard deviation of d (d is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than d?
(A) (-6;0)
(B) (0;0)
(C) (0;6)
(D) (0;12)
(E) (6;6)
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers , which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
Answer: E.
Answer: (E) (6;6)
Question: Integer X represents the product of all integers between 1 to 28 (inclusive). The smallest prime factor of (x+1) must be
(A) Between 1 to 10
(B) Between 11 to 15
(C) Between 15 to 20
(D) Between 20 to 28
(E) Greater than 28
Rationale: Answer = E = Greater than 28
This problem is asking smallest prime factor of (28!+1)
28! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor)
Just adding 1 to 28! will remove all the factors stated above;
so the smallest possible prime factor has to be greater than 28
Answer = E
Answer: (E) Greater than 28
Question: 45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) 74
(B) 55
(C) 44
(D) 75
(E) 72
Rationale: B
55
(45 * 8)/30 = (x * 6)/50 => x =100
100 – 45 = 55
Answer: (B) 55
Question: In a division, a student took 48 as divisor instead of 36. his answer was 24 . The correct answer is-
(A) 42
(B) 32
(C) 48
(D) 28
(E) 38
Rationale: X/48 = 24.
X = 24 *48.
So correct answer would be,
(24 *48) /36 = 32.
ANSWER : B
Answer: (B) 32
Question: Find the odd man out. 187, 264, 316, 473, 682, 781
(A) 187
(B) 316
(C) 781
(D) 682
(E) 473
Rationale: In all numbers except 316, the middle digit is the sum of other two digits.Answer is B
Answer: (B) 316
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 500 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
(A) 2880.
(B) 3600.
(C) 5780
(D) 5760
(E) 6380.
Rationale: Normal Day = 500 kw/h
Stormy Day = 500*1.2=600 kw/h
3 windmills for 2 hours on stormy day
600*3*2=3600
Answer: B
Answer: (B) 3600.
Question: John works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 6 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
(A) 1/8
(B) 1/7
(C) 1/2
(D) 1/4
(E) 1/6
Rationale: First notice the number of months for which he worked - March to Sept i.e. 7 months
Avg of monthly totals in tips for months other than August = x
Tips in August = 6x
Total tips for all months = 6*x + 6x = 12x
Tips for August/Total tips for all months = 6x/12x = 1/2
Answer : C
Answer: (C) 1/2
Question: When the airplane moves at an average speed of 450 kmph it reaches its destination on time. When its average speed becomes 400 kmph, then it reaches its destination 30 minutes late. Find the length of journey.
(A) 1250 km
(B) 1500 km
(C) 1100 km
(D) 1800 km
(E) None
Rationale: Sol.
Difference between timings = 30 min = 1/2 hr.
Let the length of journey be x km.
Then, x/400 - x/450 = 1/2
â‡” 9x - 8x = 1800
â‡” x = 1800 km.
Answer D
Answer: (D) 1800 km
Question: A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in?
(A) 30.4 sec
(B) 40.4 sec
(C) 60.4 sec
(D) 50.4 sec
(E) 80.4 sec
Rationale: D
50.4 sec
Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 770 m
Time = Distance / Speed
= 770 x 18 / (5 x 55)
= 50.4 sec
Answer: (D) 50.4 sec
Question: An order was placed for supply of carpeat of breadth 3 metres the length of carpet was 1.44 times of breadth. Subsequently the breadth and length were increased by 25 and 40 percent respectively. At the rate of Rs.45 per square metre, what would be the increase in the cost of the carpet?
(A) Rs.1020.6
(B) Rs.398.8
(C) Rs.437.4
(D) Rs.583.2
(E) Rs.354.6
Rationale: Explanation:
Initial area of the carpet = 3 x 3 x 1.44 = 12.96 sq.metres.
Increased area = 3 + 3 x 25/100 x 3 x 1.44/100 + 3 x 1.44 x 40/100
= 375 x 604.8/ 100 x 100 = 22.68 sq.metre
:. Increase in area = 22.68 – 12.96 = 9.72 sq.metre.
Cost of 9.72 sq.metre = 9.72 x 45 = Rs.437.40
Answer: Option C
Answer: (C) Rs.437.4
Question: Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 35 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam.
After 40 minutes Annie is 2 km ahead.
Sam rides 1 km every 5 minutes.
In the next 35 minutes, Sam rides 7 km so Sam will be 5 km ahead.
It will take Annie 100 minutes to catch Sam.
The answer is E.
Answer: (E) 100
Question: A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 930gm. for a kg.His gain is …%.
(A) 5.26%
(B) 5.36%
(C) 4.26%
(D) 6.26%
(E) 7.53%
Rationale: His percentage gain is 100*7/930 as he is gaining 70 units for his purchase of 930 units.
so 7.53%.
ANSWER:E
Answer: (E) 7.53%
Question: 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = ½
=> 52m + 96b = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
= 15/100 + 20/200 =1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days
Answer is A.
Answer: (A) 4
Question: A watch was sold at a loss of 36%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 350
(B) 288
(C) 799
(D) 778
(E) 901
Rationale: 64%
104%
--------
40% ---- 140
100% ---- ? => Rs.350
Answer: A
Answer: (A) 350
Question: Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 3 times, and no one scored below 510 or over 780. If the individual ranges of the three people's scores in those 3 practice tests were 20, 90 and 130, what is the difference between the maximum and minimum possible ranges of all their scores put together.
(A) 70
(B) 80
(C) 90
(D) 140
(E) 170
Rationale: According to the information in the question the maximum range would be between 510 and 780(270). The minimum range would be the greatest range for any one individual, which is listed in the problem as 130. So the difference between these would be 270-130 or 140.
Answer: D
Answer: (D) 140
Question: The speed of the boat in still water in 12 kmph. It can travel downstream through 48 kms in 3 hrs. In what time would it cover the same distance upstream?
(A) 8 hours
(B) 6 hours
(C) 4 hours
(D) 5 hours
(E) 6 hours
Rationale: Still Water=12km/hr
Downstream=48/3=16km/hr
Upstream=>> still water=(u+v/2) =>> 12=u+16/2 = 8km/hr
So time taken in upstream = 48/8 =6hrs
ANSWER:E
Answer: (E) 6 hours
Question: Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
(A) 9680
(B) 2288
(C) 7799
(D) 1777
(E) 2991
Rationale: (8000*3*2)/100 = 480
9200
--------
9680
Answer:A
Answer: (A) 9680
Question: A car dealer sold x used cars and y new cars during May. If the number of used cars sold was 10 greater than the number of new cars sold. Which of the following expresses this relationship ?
(A) x > 10y
(B) x > y + 10
(C) x > y – 10
(D) x = y + 10
(E) x = y – 10
Rationale: Given: x used cars and y new cars
Number of used cars (x) sold was 10 greater than the number of new cars (y) sold
So, x is 10 greater than y
To show their relative sizes let's write x LARGER than y to get: x and y
Our goal is to create an EQUATION. So, how do we make these two values EQUAL?
Well, we need to make the smaller value (y) bigger. 10 bigger to be exact.
So, we get x = y + 10
Answer: D
Answer: (D) x = y + 10
Question: A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices.
(A) 255
(B) 816
(C) 192
(D) 100
(E) 144
Rationale: Two cases.
First Case: 2 Questions - 3 Choices, 2 Questions - 4 Choices
2C2 * 3C2 ways to select the questions
3C1 * 3C1 * 4C1 * 4C1 ways to answer the questions
= 1 * 3 * 3 * 3 * 4 * 4
= 27 * 16
= 432
Second Case: 1 Question - 3 Choices, 3 Questions - 4 Choices
2C1 * 3C3 ways to select the questions
3C1 * 4C1 * 4C1 * 4C1 ways to answer the questions
= 2 * 1 * 3 * 4 * 4 * 4
= 6 * 64
= 384
Total = 384 + 432
= 816
ANS:B
Answer: (B) 816
Question: How many unique positive odd integers less than 70 are equal to the product of a positive multiple of 5 and an odd number?
(A) 4
(B) 7
(C) 11
(D) 12
(E) 15
Rationale: The Question basically asks how many positive odd integers less than 70 are odd multiples of 5
So we have 5,15,25,35,45,55 and 65
=7
Ans B
Answer: (B) 7
Question: if m<0 and x is m percent of y, then, in terms of m, y is what percent of x?
(A) a)10^4m
(B) b)1/100m
(C) c)1/m
(D) d)10/m
(E) e)10,000/m
Rationale: Given (m*y)/100=x
to find (y/x)*100
Rearranging first equation
y/x*100 = 100*100/m
=10000/m
Answer A
Answer: (A) a)10^4m
Question: A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 14 km per hour and the level part at the rate of 21 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 21 km per hour for the entire route?
(A) 28
(B) 35
(C) 42
(D) 49
(E) 56
Rationale: Let V be the speed on the downhill section.
Let D be the distance of each of the three equal sections.
Total time T = T1+T2+T3 and 3D/T = 21 km/hour
3D / (D/14 + D/21 + D/V) = 21
1/7 = 1/14 + 1/21 + 1/V
1/V = 1/42 and so V = 42 km/h
The answer is C.
Answer: (C) 42
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) 6
(B) 5
(C) 9
(D) 7
(E) 2
Rationale: 7 * 8 : 9 * x = 8:9
=> x= 7
Answer:D
Answer: (D) 7
Question: Fine the volume of cuboid 15 m length, 9 m breadth and 2 m height.
(A) 1440
(B) 1540
(C) 1140
(D) 1220
(E) 1330
Rationale: l × b × h => 15 × 12 × 8 = 1440 m(power3)
Answer is A
Answer: (A) 1440