mathewhe/aqua_rat huggingface dataset:
Question: Here are 5 Rock songs, 6 Carnatic songs and 3 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?
(A) 15624
(B) 1634
(C) 16144
(D) 240
(E) 3214
Rationale: There are 2n ways of choosing ‘n’ objects. For e.g. if n = 3, then the three objects can be chosen in the following 23 ways - 3C0 ways of choosing none of the three, 3C1 ways of choosing one out of the three, 3C2 ways of choosing two out of the three and 3C3 ways of choosing all three.
In the given problem, there are 5 Rock songs. We can choose them in 25 ways. However, as the problem states that the case where you do not choose a Rock song does not exist (at least one rock song has to be selected), it can be done in 25 - 1 = 32 - 1 = 31 ways.
Similarly, the 6 Carnatic songs, choosing at least one, can be selected in 26 - 1 = 64 - 1 = 63 ways.
And the 3 Indi pop can be selected in 23 = 8 ways. Here the option of not selecting even one Indi Pop is allowed.
Therefore, the total number of combinations = 31 * 63 * 8 = 15624
Option A
Answer: (A) 15624
Question: A football coach must choose 5 freshers from a team of 12players. How many different ways can the coach choose the freshers?
(A) 500
(B) 650
(C) 729
(D) 800
(E) 890
Rationale: Choose 5 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{5}}= 729
C
Answer: (C) 729
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is?
(A) 9! * ⁷P₆
(B) 6! * ⁷P₆
(C) 7! * ⁷P₆
(D) 6! * ⁷7₆
(E) 2! * ⁷P₆
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆
Answer:B
Answer: (B) 6! * ⁷P₆
Question: What is the smallest integer k for which 64^k > 4^17?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 64^k > 4^17
4^(3k) > 4^17
3k > 17
k = 6
The answer is C.
Answer: (C) 6
Question: Three interviewers, X, Y, and Z are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer X admitted 15 applicants, Y admitted 17 applicants, and Z admitted 20 applicants, at least how many applicants get the admission?
(A)  0
(B)  2
(C)  6
(D)  8
(E)  12
Rationale: If X admitted 15 are overlapping with Y admission of 17 But Z does not overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.
Answer : A
Answer: (A)  0
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19.7
(B) 20
(C) 23
(D) 25
(E) 27
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A)
Answer: (A) 19.7
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 33 days
(B) 77 days
(C) 30 days
(D) 17 days
(E) 18 days
Rationale: C = 1/5 – 1/6 = 1/30 => 30 days
Answer:C
Answer: (C) 30 days
Question: How many prime numbers are between 29/4 and 87/5?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 29/4 = 7.xxx
87/5 = 17.xxx
So we need to find Prime numbers between 7 (Exclusive) - 16 (Inclusive)
There are 2 Prime numbers 1113
Hence answer will be (B) 2
B
Answer: (B) 2
Question: If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 82?
(A) 11
(B) 12
(C) 13
(D) 20
(E) 25
Rationale: four wheeler=20*4=80(max)
2 wheel=1
so no of 4 wheeler=20
ANSWER:D
Answer: (D) 20
Question: If m is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2) must be a multiple of which one of the following is correct?
(A) 2
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: (D) 7
Question: A train running at the speed of 48 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 140
(B) 130
(C) 120
(D) 170
(E) 160
Rationale: Speed=(48x5/18)m/sec = (40/3) m/sec.
Length of the train = (Speed x Time).
Length of the train = (40/3 x 9)m = 120 m.
Answer is C.
Answer: (C) 120
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 20 percent of the drive from the center, what percent of the round-trip has the technician completed?
(A) 60
(B) 50
(C) 40
(D) 70
(E) 45
Rationale: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 20% of 50% i.e 10%. so he completed 50 +10 =60 % of total trip
A
Answer: (A) 60
Question: A line that passes through (–3, –4) and (3, k) has a slope = k. What is the value of k?
(A)  3/4
(B)  1
(C)  4/5
(D)  2
(E)  7/2
Rationale: Slope = (y2-y1)/(x2-x1)
=> k = (k+4)/(3+3)
=> 6k = k+4
=> k =4/5
Ans C it is!
Answer: (C)  4/5
Question: The monthly rent of a shop of dimension 18feet × 20feet is Rs.3600. What is the annual rent per square foot of the shop?
(A) 120
(B) 56
(C) 68
(D) 87
(E) 92
Rationale: Sol. Monthly rent per square feet = 3600/(18*20) = 10
& Annual rent per square feet
=12*10=120
Answer : A
Answer: (A) 120
Question: If A = {10, 15, 18, 22, 36, 44}, what is the product of mean and median of the numbers in A?
(A) 105
(B) 245
(C) 360
(D) 480
(E) 542
Rationale: Mean = (10 + 15 +18 + 22 + 36 + 43)/6 = 24
Median = (18+22)/2 = 20
product = 24*20 = 480
Option D
Answer: (D) 480
Question: What is the sum of the different positive prime factors of 650?
(A) 9
(B) 10
(C) 15
(D) 17
(E) 20
Rationale: The prime factorization of 650
= 65 * 10
= 5*13 * 2*5
The sum of the different positive prime factors = 2+5+13 = 20
The answer is E.
Answer: (E) 20
Question: In Orange County, one eighth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
(A) 200
(B) 210
(C) 216
(D) 224
(E) 235
Rationale: The number must be a multiple of both 8 and 7 so the answer is 224.
The answer is D.
Answer: (D) 224
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 8 p.c?
(A) 36800
(B) 38000
(C) 32977
(D) 38128
(E) 38982
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(92/100)
= 36800
Answer:A
Answer: (A) 36800
Question: A board of length L feet is cut into two pieces such that the length of piece A is 2 feet less than twice the length of piece B. Which of the following is the length, in feet, of piece A ?
(A) (L - 1)/2
(B) (2L + 1)/3
(C) (L + 1)/3
(D) (2L + 2)/3
(E) (2L - 2)/3
Rationale: A+B = L so we know that B = L - A.
A = 2B-2
A = 2(L-A) - 2
3A = 2L - 2
A = (2L-2) / 3
The answer is E.
Answer: (E) (2L - 2)/3
Question: An observation is made on a clock and it is found that the hour hand is placed exactly at the minute mark while the minute hand is six minutes ahead it. After some time, the clock is observed again and it is found that the hour hand is exactly on another minute mark while the minute hand is seven minutes ahead of it.
Analyzing this data, can you calculate the total time that has elapsed between the two observations?
(A) 2hr 11min
(B) 1hr 11min
(C) 3hr 11min
(D) 2hr 15min
(E) 3hr 21min
Rationale: A
Now this question cannot be solved unless you know a fact i.e. the hour hand is exactly on the minute mark five times every hour - on the hour, 12 minutes past hour, 24 minutes past hour, 36 minutes past hour and 48 minutes past hour.
Denoting the number of hours with X and the number of minutes as Y, let us begin with the calculation.
When we have the hour hand on the minute mark, the position of hour hand:
5X + Y/12
And the position of the minute hand = Y
When the first observation was taken,
Y = Y = 5X + Y/12 + 6
Or, 60X = 11Y - 72.
With the given facts, we know for sure that Y can only be 0, 12, 24, 36 or 48.
According to which, the possible values for X and Y can be 1 and 12 respectively. Thus the time must be 1:12 when the first observation was taken.
Similarly, in the second observation, let's make the equation:
60X = 11Y - 84
Here, the possible values for X and Y here are 3 and 24 respectively. According to this, the time is 3:24 for sure.
From 1:12 to 3:24, two hours and eleven minutes have passed.
Answer: (A) 2hr 11min
Question: The day of week on July 1,2000 was
(A) Monday
(B) Friday
(C) Saturday
(D) Tuesday
(E) None of the above
Rationale: 1600 years:0 odd days
300 years=1 odd day
99 years=4 odd days
So till 1999 there are 5 odd days
now in 2000....2000 is a leap year
1 odd day till 1 july 2000 from jan 1 2000
so total odd days=5+1=6
So saturday
ANSWER:C
Answer: (C) Saturday
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases?
(A) 8:8
(B) 8:1
(C) 8:7
(D) 8:5
(E) 8:9
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8:7
Answer:C
Answer: (C) 8:7
Question: The average waight of A,B,C is 45 Kg. The avgwgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.
(A) 23 KG
(B) 43 KG
(C) 21 KG
(D) 31 KG
(E) 43 KG
Rationale: Sol. Let A,B,c represent their individual wgts.
Then,
A+B+C=(45*3)Kg=135Kg
A+B=(40*2)Kg=80Kg & B+C=(43*2)Kg=86Kg
B=(A+B)+(B+C)-(A+B+C)
=(80+86-135)Kg
=31Kg.
ANSWER D
Answer: (D) 31 KG
Question: If 6x^2 + x - 12 = (gx + b)(cx + d), then |g| + |b| + |c| + |d| =
For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/
(A)  10
(B)  12
(C)  15
(D)  18
(E)  20
Rationale: 6x^2+x-12 = 6x^2 + 9x -8x -12
=> 3x(2x+3) -4(2x+3)
=> (2x+3)(3x-4) = (gx+b)(cx+d)
Hence g=2, b=c=3, d=-4
So, 2+3+3+ |-4| = 2+3+3+4 = 12
Answer B.
Answer: (B)  12
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 40% ?
(A)  2.1
(B)  1.9
(C)  1.7
(D)  1.5
(E)  1.6
Rationale: Let x be the number of males.
Total contestants = 10
Probability that the first contestant selected is a male = x/10
Probability that the second contestant selected is also a male = x-1/9
Total probability = x(x-1)/ 90 < 1/40 (this probability is less than 40%)
Solving for x we get, x(x-1)< 9/4. This implies that the maximum value of x can be 1.5.
Answer D!
Answer: (D)  1.5
Question: What is the speed of the stream if a canoe rows upstream at 6km/hr and downstream at 10km/hr
(A) 1 kmph
(B) 4 kmph
(C) 3 kmph
(D) 2 kmph
(E) 1.9 kmph
Rationale: Sol.
Speed of stream = 1/2(10 -6) kmph = 2 kmph.
Answer D
Answer: (D) 2 kmph
Question: Preethi has 6 flavors of ice cream in his parlor. How many options are there for Dorathy to pick a one-flavor, two-flavor, three-flavor, four-flavor, five flavor or six flavor order?
(A) 26
(B) 36
(C) 64
(D) 67
(E) 63
Rationale: 6C1 + 6C2+ 6C3+6C4+6C5+6C6 = 63.
Answer: E
Answer: (E) 63
Question: A is 30% more efficient than B .how much time they will working together take to complete a job which A alone could have done in 23 days?
(A) 25 days
(B) 13 days
(C) 14 days
(D) 20 days
(E) 15 days
Rationale: The ratio of times taken by A and B=100:130=10:13
suppose B can do work in x days
then 10:13::23:x
x=(23*13)/10
x=299/10
A's 1 day's work=1/23
B's 1 day's work=10/299
(A+B)'s 1 day's work =1/23+10/299 =23/299=1/13
A and B together can do work in 13 days
Answer(B)
Answer: (B) 13 days
Question: A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance W between the two cities?
(A) 48
(B) 72
(C) 96
(D) 120
(E) 192
Rationale: Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance W to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E
Answer: (E) 192
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
(A) 1:1
(B) 2:3
(C) 3:2
(D) 9:4
(E) 27:8
Rationale: Water:soap = 3:2
Soap:Salt=9:2
=> For 9 soap, salt = 2
=> For 2 Soap, salt = (2/9)*2 = 4/9
So, water:soap:salt = 3:2:4/9 = 27:18:4
After open container, water:soap:salt = 13.5:18:4
So, water:salt = 13.5:4 = 27:8
ANSWER:E
Answer: (E) 27:8
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?
(A) 278
(B) 277
(C) 960
(D) 278
(E) 261
Rationale: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer:C
Answer: (C) 960
Question: The traffic lights at three different road crossings change after every 48 sec., 72 sec and 108 sec.respectively .If they all change simultaneously at 8:20:00 hours,then at what time they again change simultaneously .
(A) 8:29:12 hrs
(B) 8:22:12 hrs
(C) 8:25:12 hrs
(D) 8:27:12 hrs
(E) 8:21:12 hrs
Rationale: Interval of change = (L.C.M of 48,72,108)sec.=432sec.
So, the lights will agin change simultaneously after every 432 seconds i.e,7 min.12sec
Hence , next simultaneous change will take place at 8:27:12 hrs
Answer is D.
Answer: (D) 8:27:12 hrs
Question: Find the missing value?
19 28 23 32
40 31 36 27
? 44 39 48
(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: 19 (+9) 28 (-5) 23 (+9) 32
40 (-9) 31 (+5) 36 (-9) 27
? (+9) 44 (-5) 39 (+9) 48
hence ?+9=44
?=35
ANSWER:E
Answer: (E) 35
Question: Rs. 1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
(A) 300
(B) 992
(C) 772
(D) 552
(E) 312
Rationale: 1/2:1/3:1/4 = 6:4:3
3/13*1300 = 300
Answer: A
Answer: (A) 300
Question: Two pens and three pencils cost Rs 86. four Pens and a pencil cost Rs. 112. find the cost of a pen and that of a pencil.
(A) 12
(B) 10
(C) 15
(D) 19
(E) 20
Rationale: Let the cost of a pen ands a pencil be Rs. X and Rs. Y respectively.
Then, 2x + 3y = 86 ….(i) and 4x + y =112.
Solving (i) and (ii), we get: x = 25 and y = 12.
Cost of a pen =Rs. 25 and the cost of a pencil =Rs. 12.
Answer is A.
Answer: (A) 12
Question: The cost price of an article is 70% of the marked price. Calculate the gain percent after allowing a discount of 10%.
(A) 13.6%
(B) 28.6%
(C) 35.6%
(D) 42.3%
(E) none
Rationale: Sol.
Let marked price = Rs. 100. Then, C.P. = Rs. 70. S.P = Rs. 90.
âˆ´ Gain % = [20/70 * 100]% = 28.6%.
Answer B
Answer: (B) 28.6%
Question: Solve the quickfire maths brain teaser âˆš49% = ?
(A) 30%
(B) 40%
(C) 70%
(D) 19%
(E) 29%
Rationale: âˆš49%
=> âˆš49/âˆš100
=> 7/10
=> 70/100
=> 70%
C
Answer: (C) 70%
Question: There are 13person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
(A) 4!*2!
(B) 7!*2!
(C) 6!*1!
(D) 10!*2!
(E) 5!*1!
Rationale: Total number of ways = 10!*2!.
D
Answer: (D) 10!*2!
Question: The probability of selecting face card of any color from 52 cards
(A) 1/13
(B) 2/13
(C) 3/13
(D) 4/13
(E) 5/13
Rationale: king queen and jack are the face cards
there are totally 12 face cards in a suit
probability = 12/52 = 3/13
ANSWER:C
Answer: (C) 3/13
Question: If a certain number is divisible by 36 and 52, it is NOT necessarily divisible by which of the following?
(A) 4
(B) 6
(C) 13
(D) 16
(E) 18
Rationale: If a certain number is divisible by 36 and 52, it is NOT necessarily divisible by which of the following?
let the certain number be 468, which is both divisible by 36 and 52.
468/16 =117/4
D. 16
Answer: (D) 16
Question: A lady builds 8cm length, 15cm width, and 5cm height box using 10cubic cm cubes. What is the minimum number of cubes required to build the box?
(A) 107
(B) 60
(C) 70
(D) 89
(E) 78
Rationale: Number of cubes required = Volume of box/Volume of cube
= 8*15*5/10
=60 cubes
ANSWER:B
Answer: (B) 60
Question: A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random form this box. The probability that at least one of these is defective is:
(A) 10/19
(B) 7/19
(C) 17/19
(D) 19/19
(E) 14/19
Rationale: P(none is defective)=16c2/20c2
=12/19
P( at least one is defective)= 1-12/19
=7/19
ANSWER B 7/19
Answer: (B) 7/19
Question: Working together at their respective constant rates, Machine A and Machine B can produce 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 600 unit total would it produce?
(A) 25
(B) 37
(C) 50
(D) 30
(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 600 units in 24 hrs, so it can produce 600*8/24= 200 units is 8 hrs.
200 is 30% of 600.
D is the answer
Answer: (D) 30
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150m
(B) 159m
(C) 750m
(D) 180m
(E) 159m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:A
Answer: (A) 150m
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?
(A) $1
(B) $1.84
(C) $2.54
(D) $2.65
(E) $3
Rationale: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Answer: (B) $1.84
Question: Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?
(A) 2/5521
(B) 2/5529
(C) 5525/2
(D) 1/5525
(E) 2/5525
Rationale: Let Q denote the event that the card drawn is queen and A be the event that
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51
P(A|QQ) is the probability of third drawn card to be an ace, with the condition
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50
By multiplication law of probability, we have
P(QQA) = P(Q) P(Q|Q) P(A|QQ)
= 4/52 × 3/51 × 4/50
= 2/5525.
E
Answer: (E) 2/5525
Question: NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day.if in 25 days they completed 1/3 part of work .than how many more emploies should NHAI hire to finish it in time working 10 hours a day
(A) 60
(B) 70
(C) 80
(D) 50
(E) 40
Rationale: (M1*D1*H1)/W1 = (M2*D2*H2)/W2
(100*25*8)/(1/3) =((100+a)*25*10))/(2/3)
160=100+a
a=60
ANSWER:A
Answer: (A) 60
Question: n what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
(A) 2/7
(B) 5/6
(C) 3/4
(D) 1/5
(E) 6/16
Rationale: Explanation:
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Correct Option :B
Answer: (B) 5/6
Question: The wages earned by Robin is 38% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?
(A) 23%
(B) 27.53%
(C) 30%
(D) 50%
(E) 100%
Rationale: Explanatory Answer
Let the wages earned by Erica be $100
Then, wages earned by Robin and Charles will be $138 and $160 respectively.
Charles earns $38 more than Robin who earns $138.
Therefore, Charles' wage is 38/138*100 = 27.53%.
The correct choice is (B)
Answer: (B) 27.53%
Question: There are three departments having students 68,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
(A) 73
(B) 74
(C) 75
(D) 76
(E) 77
Rationale: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 68/2 = 34
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 34+12+29 = 75
ANSWER:C
Answer: (C) 75
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o'clock noon?
(A) 30
(B) 60
(C) 90
(D) 120
(E) 150
Rationale: The hour hand will move 4/12 of a circle.
(4/12)*360 = 120 degrees.
The answer is D.
Answer: (D) 120
Question: Which of the following integers is the square of an integer?
(A) 73,410,624
(B) 63,398,748
(C) 54,113,892
(D) 42,785,337
(E) 31,298,793
Rationale: CONCEPT: The unit digit of any Perfect Square can't be 2 or 3 or 7 or 8
Hence Option B, C D and E can be ruled out
Answer: option A
Answer: (A) 73,410,624
Question: The perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
(A) A)40
(B) B)828
(C) C)729
(D) D)34
(E) E)35
Rationale: Explanation:
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 32/2 = 40 cm2
Answer: Option A
Answer: (A) A)40
Question: A coin is tossed 4 times. What is the probability t that the number of Heads is equal to the number of Tails?
(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 9/16
Rationale: We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.
Using the binary formula and defining a head as a success,
P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2
t= 6/16
= 3/8
The answer is therefore (C)
Answer: (C) 3/8