mathewhe/aqua_rat huggingface dataset:
Question: (2^2-1)(2^2+1)(2^4+1)(2^12+1)=
(A) 2^20 - 1
(B) 2^16 + 1
(C) 2^32 - 1
(D) 2^128 - 1
(E) 2^16(2^16-1)
Rationale: A: is correct
(2^2-1)* (2^2+1)=(2^4-1)
(2^4-1)*(2^4+1)=2^8-1
(2^8-1)*(2^12 +1)=2^20-1
You can apply to this formula: a^2- b^2=(a-b)*(a+b)
Answer: (A) 2^20 - 1
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 6 times, what is the probability that it will land heads up on the first 3 flips but not on the last 3 flips?
(A) 1/8
(B) 1/16
(C) 1/32
(D) 1/64
(E) 1/128
Rationale: P(HHHTTT) = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64
The answer is D.
Answer: (D) 1/64
Question: If a jar contains 25 percent red candies, 10 percent blue candies, and 55 white candies, what fraction of candies are of another color?
(A) 4/5
(B) 3/5
(C) 3/10
(D) 1/5
(E) 1/10
Rationale: 100%-(25%+10%+55%)=10% of candies are another color --> 10% = 10/100 = 1/10.
Answer: E.
Answer: (E) 1/10
Question: Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of a gamma raised to the seventh power and a delta raised to the seventh power?
(A) alpha
(B) beta
(C) gamma
(D) delta
(E) epsilon
Rationale: Solution : 2 is gamma and 3 is a delta. 2^7 + 3^7 will have a units digit as 8+7=5. So, label is alpha.
or
alpha : 5k
beta : 5k +1
gamma : 5K+2
delta : 5k+3
epsilon : 5K+4
(5k + 2)^7 has unit digit as 8 or 3
(5k + 3)^7 has unit digit as 7 or 2
In any case (5k + 2)^7 + (5k + 3)^7 will have units digit as 0 or 5 which is a alpha.
Option A
Answer: (A) alpha
Question: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have
(A)  4
(B)  6
(C)  9
(D)  10
(E)  12
Rationale: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides
A
Answer: (A)  4
Question: If a person sells a wooden furniture at 8% profit against 8% loss, then he could had earned Rs12 more. What is the cost price of furniture?
(A) 72
(B) 70
(C) 80
(D) 75
(E) None
Rationale: Answer
Let Cost Price (CP) = x
Then Selling Price(SP) if he sells at profit = x(1+8%) = 1.08x
and SP, if he sells at loss = x(1-8%) = 0.92%
Given, 1.08%-0.92% = Rs12
0.16x = Rs.12
⇒x = Rs.75
Correct Option: D
Answer: (D) 75
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 21 (1/8)
(B) 21 (1/3)
(C) 21 (7/3)
(D) 22 (1/3)
(E) 31 (1/3)
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.
Answer: B
Answer: (B) 21 (1/3)
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1395 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) Rs. 4500
(B) Rs. 4800
(C) Rs. 5250
(D) Rs. 7626
(E) None of these
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1395
45k = 1395 => k = 31
246k = 246(31) = Rs. 7626
Thus the total rent paid by all the four agencies is Rs. 7626.
ANSWER:D
Answer: (D) Rs. 7626
Question: A person purchased a TV set for Rs. 14000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 16.82%
(B) 87.82%
(C) 53.82%
(D) 17.82%
(E) 18.82%
Rationale: The total CP = Rs. 14000 + Rs. 6250 = Rs. 20250 and SP
= Rs. 31150
Profit(%) = (31150 - 20250)/20250 * 100
= 53.82%
Answer:C
Answer: (C) 53.82%
Question: Lilly has 10 fish and Rosy has 12 fish. In total, how many fish do they have in all?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 26
Rationale: 10+12=22
The answer is C.
Answer: (C) 22
Question: 33 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 11
(C) 13
(D) 18
(E) 19
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 33 :: 12 : x
Working hours/day 6 : 5
30 x 6 x x = 33 x 5 x 12
x = (33 x 5 x 12)/(30 x 6)
x = 11
ANSWER B
Answer: (B) 11
Question: If x+y=-4, and x=6/y, what is the value of x^2+y^2?
(A) 10
(B) 15
(C) 6
(D) 4
(E) 5
Rationale: x^2 + y^2 should make you think of these formulas:
(x+y)(x+y) = x^2+y^2+2xy
We already know (x+y) = -4 and x*y = 6
(x+y)(x+y) = (-4)(-4) = x^2+y^2+2*(6)
x^2+y^2 = 16 - 12 = 4
Answer : D
Answer: (D) 4
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
(A) 3/6
(B) 3/2
(C) 3/3
(D) 3/5
(E) 5/2
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train
= 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y
==> 4 x = 6 y ==> x/y
= 3/2.
Answer:B
Answer: (B) 3/2
Question: During the last 5 days, John ran 5 miles per day on average. How many miles must he run tomorrow to increase his daily average to 7 miles per day.
(A) 2
(B) 7
(C) 17
(D) 30
(E) 32
Rationale: Solution
Average after 6 days = 7
âˆ´ Required miles to run= (6 days x 7 miles/day)-(5 days x 5 miles/day)
= 42 - 25
= 17.
Answer C
Answer: (C) 17
Question: A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares?
(A) $37.5
(B) $40
(C) $50
(D) $48
(E) $52
Rationale: Dividend on 1 share = $(10/100*50)
=$5
$12.5 is an income on an investment of $100
$5 is an income on an investment of $(100*2/25*5)=40
Thus, cost of 1 share =$40
option B
Answer: (B) $40
Question: If m > 1 and n = 2^(m+3), then 4^m =
(A) 16n^2
(B) 4n^2
(C) 8n^2
(D) n^2/64
(E) n^2/16
Rationale: n = 2^(m+3) = 2^m*8
2^m = n/8
4^m = (2^m)^2 = (n/8)^2 = n^2/64
The answer is D.
Answer: (D) n^2/64
Question: A party supply store sells noisemakers arranged on display such that each of the three different colors of noisemakers, red, blue, and purple are consecutive in a repeating pattern. If four consecutively displayed noisemakers are purchased, what is the probability that two of the noisemakers are purple?
(A) 2/3
(B) 1/9
(C) 2/9
(D) 1/3
(E) 2/7
Rationale: After red, blue, and purple, the next noisemakers can be of any given three colours, therefore we have total three possibilites, out of which we need purple i.e. 1 therefore prob is 1/3. Correct answer is D.
Answer: (D) 1/3
Question: if A fills a tank in 30mins,and B fills the same tank in 20mins,and C emptys it in 40min ,if A,B,C works together how much time will the tank take to fill?
(A) 15.14mins
(B) 16.14mins
(C) 17.14mins
(D) 18.14mins
(E) 19.14mins
Rationale: 1/30+1/20-1/40=7/120
so total time=120/7
=17.14mins
ANSWER:C
Answer: (C) 17.14mins
Question: In how many ways can 5 men & 4 women can be made from a gang of 6 men & 6 women ?
(A) 10
(B) 21
(C) 24
(D) 27
(E) 29
Rationale: Explanation:
6C5* 6C4 = 21
B
Answer: (B) 21
Question: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the sixth digit of p, counting right to left from the units digit?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 9
Rationale: C
Sum of unit digits of first 30 terms = 60
Sum of tens digits of first 30 terms = 58
Sum of thousands digits of first 30 terms = 56
and so on..
p1 = 0
p2 = (6+58) = 4
p3 = (6+56) = 2
p4 = (6+54) = 0
p5 = (6+52) = 8
p6 = (5+50) = 5
ANSWER :D
Answer: (D) 5
Question: A train sets off at 2 p.m. at the speed of 80 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
(A) 3.30 p.m.
(B) 4.30 p.m.
(C) 3.50 p.m.
(D) 9.30 p.m.
(E) 8.30 p.m.
Rationale: D = 80 * 1 ½ = 120 km
RS = 85 – 80 = 5
T = 120/5 =24 h
3.30 + 24 h =3.30 p.m.
ANSWER:A
Answer: (A) 3.30 p.m.
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
(A) 40%
(B) 50%
(C) 55%
(D) 60%
(E) 70%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50%
B
Answer: (B) 50%
Question: Carrie likes to buy t-shirts at the local clothing store. They cost $9.95 each. One day, she bought 25 t-shirts. How much money did she spend?
(A) $150
(B) $248.75
(C) $200
(D) $171.6
(E) $190
Rationale: $9.95*25=$248.75. Answer is B.
Answer: (B) $248.75
Question: The value of land increases by a% during June and decreases by b% during July. If the value of the land is the same at the end of July as at the beginning of June, what is b in terms of a?
(A) 200a/(100+2a)
(B) 100a/(100+a)
(C) a(2+a)/(1+a)2
(D) a(200+a)/10000
(E) 2a/a+2a
Rationale: let the value of land be : x
it is increased by a%, new value= (x)+(ax/100)
now, it is decreased by b%, such that it equals the initial value
hence final value of land= x(1+a/100) - x(1+a/100)(b/100)= x(1+a/100)(1-b/100)=x
solving for b you get b=100a/(100+a)
ANSWER:B
Answer: (B) 100a/(100+a)
Question: A certain car can travel 20 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 80 miles at 60 mph?
(A) 16.67%
(B) 20%
(C) 25%
(D) 30%
(E) 40%
Rationale: Let, Tank capacity = T gallon
Used Fuel = (T-8) gallons
Distance Travelled (@60 miles/hr) = 80 miles
Distance travelled in 1 gallon = Distance travelled in 20 mins (@60 miles/hr) = (60/60)*20 = 20 miles
Fuel used to travel 80 miles = (80/20) = 4 gallon
i.e. Used fuel = (T-8) = 4 gallon
i.e. T = 12 Gallons
i.e. Used Fuel = (2/12)*100 =16,67%
A
Answer: (A) 16.67%
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
(A) 52
(B) 24
(C) 27
(D) 26
(E) 28
Rationale: Let the ten's and unit digit be x and	8/x	respectively.
Then, 10x +	8/x + 18 = 10 x	8/x	+ x
10x2 + 8 + 18x = 80 + x2
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2.
Answer:B
Answer: (B) 24
Question: Average age of students of an adult school is 46 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.
(A) 1200
(B) 120
(C) 360
(D) 168
(E) None of these
Rationale: Explanation :
Let the original no. of students be x.
According to situation, 46x + 120*32 = (x + 120)36 ⇒ x = 48
So, Required no. of students after joining the new students
= x + 120 = 168.
Answer : D
Answer: (D) 168
Question: A man can row three - quarters of a kilometer against the stream in 11¼minutes. The speed(in km/hr) of the man in still water is
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Solution
Rate upstream	= (750 / 675)m/sec
= (10 / 9) m/ sec.
Rate downstream	= (750 / 450)
=(5 / 3) m/sec
Rate in still water	= 1/2(10 /9 + 5/3)
= (25/18x18/5)km/hr
= 5 km/hr.
Answer D
Answer: (D) 5
Question: In Arun's opinion, his weight is greater than 65 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?
(A) 86.5 kg
(B) 66.5 kg
(C) 46.5 kg
(D) 26.5 kg
(E) 16.5 kg
Rationale: Let Arun's weight be X kg.
According to Arun, 65 < X < 72.
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
Answer: B
Answer: (B) 66.5 kg
Question: For any positive integer n, the length of n is defined as number of prime factors whose product is n, For example, the length of 75 is 3, since 75=3*5*5. How many two-digit positive integers have length 6?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Length of a number = Total number of prime factors of the number.
Any composite number can be represented as a product of prime numbers as shown below:
N= 2^x * 3^y * 5^z * 7^a ...so on
Since our requirement is a two digit number, we shall raise maximum power for smallest prime factor.
N= 2^6 = 64 has Length 6
N= 2^5 * 3 = 96 has length 6
N=2^4 * 3^2 = 144 is a three digit number and so on the other combinations would reveal 3 digit numbers.
Hence there are only 2 numbers
ANSWER:C
Answer: (C) 2
Question: Which of the following best approximates the value of q if 20^50+20^11=20^q ?
(A) 61
(B) 52
(C) 51
(D) 50
(E) 39
Rationale: We have: 20^50+20^11=20^q
==> because 20^11 > 0 --> 20^q MUST be equal or greater than 20^50 ==>q MUST be equal or greater than 50
==> Option E is out immediately.
Divide both sides by 20^q and q >= 50
We have:
20^(50-q) + 20^11/20^q = 1
Because q >= 50 ==>20^11/20^q = 0.0000xyz, that is very small,we can ignore it.
Thus, 20^(50-q) must be approximately 1
==> 50-q = 0 ==> q is approximately 50
D is the answer.
Answer: (D) 50
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
(A) 2600
(B) 2700
(C) 2900
(D) 3900
(E) 4000
Rationale: 10c=4t
15c+2t=4000
take the cost of c & t is 2000 b'coz 10c + 4t cost is same. and divid 2000 by 10 as well as 4 and get c & t cost as,
1t-500
1c-200
therefore,
12c-2400 + 3t-1500 = 3900.
answer -D
Answer: (D) 3900
Question: Two trains travelling in the same direction at 90 and 36 kmph completely pass off another in 1 minute. If the length of the first train is 300 m, what is the length of the second train?
(A) 228
(B) 266
(C) 175
(D) 99
(E) 600
Rationale: RS = 90 â€“ 36 = 54 * 5/18 = 15 mps
T = 60 sec
D = 15 * 60 = 900 m
300
--------
600 m
Answer: E
Answer: (E) 600
Question: The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
(A) 2.4%
(B) 2.6%
(C) 0.3%
(D) 2.0%
(E) 1.3%
Rationale: (1500 * R1 * 3)/100 - (1500 * R2 * 3)/100 = 13.50 4500(R1 - R2) = 1350
R1 - R2 = 0.3%
Answer:C
Answer: (C) 0.3%
Question: Find the slope of the line perpendicular to the line y = (1/3)x - 7
(A) -1
(B) -2
(C) -3
(D) -4
(E) -5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 3. If m is the slope of the line perpendicular to the given line, then
m × (1/3) = -1
Solve for m
m = - 3
correct answer C) -3
Answer: (C) -3
Question: A and B started a business investing Rs. 92,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
(A) 9:2
(B) 3:2
(C) 23:5
(D) 18:4
(E) 17:4
Rationale: A: B = 92000 : 20000
= 92 : 20
= 46 : 10
= 23 : 5
ANSWER:C
Answer: (C) 23:5
Question: On decreasing the price of a colour TV by 20%, its sale is increased by 30%. The effect on the revenue is?
(A) 4% decrease
(B) 4% increase
(C) 16% decrease
(D) 16% increase
(E) none of these
Rationale: Net% change in revenue
= ( x + y + xy/100) %
= [-20 + 30 + ( -20 x 30)/100]% or 4%
ANSWER:B
Answer: (B) 4% increase
Question: If p shirts can be purchased for q dollars, how many shirts can be purchased for r dollars?
(A) q/pr
(B) q/p
(C) pr/q
(D) p/(qr)
(E) r/(pq)
Rationale: Ans = C
Answer: (C) pr/q
Question: How many of the positive divisors of 360 are also multiples of 4 not including 360?
(A) 8
(B) 11
(C) 12
(D) 15
(E) 16
Rationale: 360 = 2^5 * 3 * 5 = (4) * 2 * 3^2 * 5
Besides (4), the exponents of 2, 3, and 5 are 1, 2, and 1.
There are (1+1)(2+1)(1+1) = 12 ways to make multiples of 4.
We must subtract 1 because one of these multiples is 360.
The answer is B.
Answer: (B) 11
Question: If (A+B) = 14, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?
(A) 16.
(B) 8.
(C) 7.
(D) 2.
(E) -2.
Rationale: Given A+B = 14 => A = 14 - B --> Eq 1
B+C = 9
C+D = 3 => D = 3 - C --> Eq 2
Then Eqs 1 + 2 => A + D = 14 - B + 3 - C
=> 17 - (B+C)
=> 17 - 9 = 8.
Option B...
Answer: (B) 8.
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 210,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?
(A) 77,500
(B) 1,860,000
(C) 2,480,000
(D) 3,360,000
(E) 4,960,000
Rationale: 210,000 × 2 × 2×2×2 = 210,000 × 16 = D
Answer: (D) 3,360,000
Question: Nine men went to a hotel. Eight of them spent Rs.1 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
(A) 19.28
(B) 10.28
(C) 11.28
(D) 14.28
(E) 17.28
Rationale: Average of 9 = x
9x = 8 * 1 + x * 2
x = 1.14
Total = 9 * 3.25 = 10.28
ANSWER:B
Answer: (B) 10.28
Question: TheOG 13thed page 193 #77 says
If n = 90! + 87, then n is divisible by which of the
following?
I. 15
II. 17
III. 19
(A)  None
(B)  I only
(C)  II only
(D)  I and II
(E)  II and III
Rationale: The example you have taken
n = 4! + 4 = 4(3!+1)
The equation gets further simplified to deviate the expected results
Try some other examples
7! + 4
9! + 5
4! + 3
Answer:B
Answer: (B)  I only
Question: A1B, D4F, H9K,then find next term ?
(A) M16Q
(B) L25P
(C) N36P
(D) N25S
(E) M9K
Rationale: By giving the number to alphabets, we get
A - B = 1-2 = -1 --> -1^2 = 1
D - F = 4-6 = -2 --> -2^2 = 4
H - K = 8-11= -3 -->-3^2 = 9
: :
: :
M - Q = 13-17=-4 --->-4^2 = 16
ANSWER:A
Answer: (A) M16Q
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 8 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 16 min. to empty
(B) 6 min. to full
(C) 9 min. to empty
(D) 9 min. to full
(E) 8 min. to full
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/8 - 1/10) = 1/40
1/40 : 2/5 :: 1 : x
x = (2/5 * 1 * 40) = 16 min.
So, the tank will be emptied in 16 min.
ANSWER:A
Answer: (A) 16 min. to empty
Question: My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 6 years of age of when my brother was born, then, what was the age of my father and mother respectively when my brother was born?
(A) 34 yrs, 23 yrs
(B) 32 yrs, 29 yrs
(C) 35 yrs, 29 yrs
(D) 35 yrs, 33 yrs
(E) none
Rationale: Sol.
Clearly, my brother was born 3 years before I was born and 6 years after my sister was born.
So, father's age when brother was born = (28 + 6) = 34 years.
mother's age when was born = (26 - 3) years = 23 years.
Answer A
Answer: (A) 34 yrs, 23 yrs
Question: A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression 2A +2B +3C?
(A) 6A+7.
(B) 5A+1.
(C) 5A-1.
(D) 7A-8.
(E) 6A-7.
Rationale: B = A-1
C= A-2
Putting these values in 2A +2B +3C we get 7A-8
D is the answer
Answer: (D) 7A-8.
Question: At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses Q at the restaurant? (Assume that all boxes are filled to capacity.)
(A) 96
(B) 240
(C) Q=256
(D) Q=384
(E) Q=480
Rationale: Most Test Takers would recognize the system of equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.
This means, at the minimum, we have...
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:
E
Answer: (E) Q=480
Question: The average of five results is 46 and that of the first four is 45. The fifth result is?
(A) 29
(B) 27
(C) 29
(D) 50
(E) 81
Rationale: 5 * 46 – 4 * 45 = 50
Answer: D
Answer: (D) 50
Question: If 3x+y=40, 2x-y=20, for integers of x and y, 4y^2=?
(A) 2
(B) 4
(C) 0
(D) 10
(E) 64
Rationale: 3x+y = 40
2x-y = 20
5x = 60
x = 12
y = 4
4y^2 = 4*16=64
Answer is E
Answer: (E) 64
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 57%
(B) 60%
(C) 65%
(D) 90%
(E) 80%
Rationale: total votes are 20400 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*11628/20400 = 57%
ANSWER:A
Answer: (A) 57%
Question: A bag contains 4red, 5blue and 3green balls. If 3 ballsare picked at random, what is the probability that both are red?
(A) 1/33
(B) 1/22
(C) 1/12
(D) 1/44
(E) 1/55
Rationale: P(Both are red),
=4C3/12C3=1/55
E
Answer: (E) 1/55
Question: Jade has 4 flavors of ice cream in his parlor. How many options are there for James to pick a one-flavor, two-flavor, three-flavor or four-flavor order?
(A) 15
(B) 13
(C) 14
(D) 17
(E) 18
Rationale: 4C1 + 4C2+ 4C3+4C4 = 15.
Answer: A
Answer: (A) 15
Question: At a special sale, 8 tickets can be purchased for the price of 6 tickets. If 8 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 8 tickets?
(A) 25%
(B) 33.3%
(C) 40%
(D) 60%
(E) 66.6%
Rationale: let the price of a ticket be Rs.100, so 6 tickets cost 600 & 8 tickets cost 800
8 tickets purchased at price of 6 tickets ie., for 600, so amount saved s Rs.200,
% of 6 tickets = (200 /800)*100 =25 %
ANSWER:A
Answer: (A) 25%
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 8 years more than the present age of Anand. Find the present age of Anand?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 8
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a - 2) => 3a - 30 = a - 2
=> 2a = 28 => a = 14.
ANSWER:C
Answer: (C) 14
Question: How long does a train 110metres long running at the speed of 72 km/hr take to cross a bridge 132metres in length?
(A) 10
(B) 11.1
(C) 12.1
(D) 31.2
(E) 21.5
Rationale: speed = 72*5/18 = 20m/s
total distance covered = 110+132 = 242m
required time = 242/20 = 12.1 sec
Answer is C
Answer: (C) 12.1