mathewhe/aqua_rat huggingface dataset:
Question: In a class, the teacher wrote a set of consecutive integers beginning with 1 on the blackboard. Little Johnny came and erased one number. The average of the remaining numbers was 2741327413. What was the number that Little Johnny erased?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: We have S = the sum of all integer from 1 to N
x = the missing integer
So as sum = average * Nb of terms
S-x= 27(4/13) * (N-1) (A)
As S-x should be an integer N-1 should be a multiple of 13.
So we have some possible scenario
N-1= 13 => N=14
N-1= 26 => N=17
N-1= 39 => N=40
N-1= 52 => N=53
....
Back to our formula (A)
x = S - 27(4/13)*(N-1)
x = (N(N+1))/2 - 27(4/13)*(N-1)
As x>0
(N(N+1))/2 > 27(4/13)*(N-1)
approx 27(4/13) by 27
(N(N+1))/2 > 27*(N-1)
N(N+1) > 54*(N-1)
So we see than N=53 is working (indeed 53*54>54*52)
So if N=53:
x = (53(54))/2 - 27(4/13)*(52)
x = (53(54))/2 - (27+4/13)*(52)
x = (53(54))/2 - 27*52-(4/13)*52
x = 53*27 - 27*52-(4/13)*52
x = 53*27 - 27*52-4*4
x = 27*(53-52) - 16
x = 27 - 16
x=11
ANSWER:C
Answer: (C) 11
Question: If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth?
(A) Rs.{(b*x)/b}
(B) Rs.{(b*x)/a}
(C) Rs.{(b*x)/j}
(D) Rs.{(b*x)/l}
(E) Rs.{(b*x)/as}
Rationale: Explanation:
Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a).
The cost of ‘b’ metres of cloth = Rs. b*(x/a) = Rs. {(b*x)/a}
ANSWER:B
Answer: (B) Rs.{(b*x)/a}
Question: A mixture of certain quantity of milk with 16 liters of water is worth 90 P per liter. If pure milk be worth Rs1.08 per liter, how much milk is there in the mixture?
(A) 100
(B) 90
(C) 80
(D) 75
(E) 70
Rationale: The mean value is 90 P and price of water is 0 P
By the alligation rule : Quantity of milk / Quantity of water
= (90 - 0) / (108 - 90)
= 90 / 18
= 5/1
proportion milk is 5/1 there in the mixture
therefore 5 * 16 = 80 liters milk is there in the mixture.
Ans - C
Answer: (C) 80
Question: Tough and Tricky questions: Arithmetic.
(56^2 + 56^2)/28^2 =
(A) 4
(B) 18
(C) 29
(D) 8
(E) 116
Rationale: Ans is 8
my approach was:
(56^2 + 56^2)/28^2 =56(56+56)/28*28
=56*112/28*28=2*4=8
D
Answer: (D) 8
Question: A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 840 in 4 years. The rate on interest per annum is.
(A) 4%
(B) 5%
(C) 6%
(D) 7%
(E) 8%
Rationale: S.I. on Rs 800 for 1 year = 40
Rate = (100*40)/(800*1) = 5%
Answer: Option B
Answer: (B) 5%
Question: A corporation ten times its annual bonus to 25 of its employees. What percent of the employees’ new bonus is the increase?
(A) 25%
(B) 44%
(C) 38%
(D) 9%
(E) 90%
Rationale: Let the annual bonus be X.
A corporation triples its annual bonus.
So new bonus = 10X.
Increase = 10X-X =9X
The increase is what percent of the employees’ new bonus
= (9X/10X)*100
= 90%
Hence E.
Answer: (E) 90%
Question: Of the 200 stamps in a collection, 80 are foreign and 50 are more than 10 years old. If 20 stamps are both foreign and more than 10 years old, how many stamps are neither foreign nor more than 10 years old?
(A) 60
(B) 90
(C) 100
(D) 130
(E) 150
Rationale: 20 stamps are both foreign and more than 10 years old.
60 stamps are foreign only.
30 stamps are 10 years old only.
The number of remaining stamps is 200 - (20+60+30) = 90
The answer is B.
Answer: (B) 90
Question: In a tennis match if the first serve is not legal, that means a fault a second serve is allowed. Normally, 20 to 40 serves are required in a set of tennis match. At the end of a set, set summary stats reveal that first serves percentage was 63%. If m out of n were first serves then m + n is equal to
(A) 1.43n
(B) 1.53n
(C) 1.63n
(D) 2.63n
(E) 3.63n
Rationale: m=n*(63/100)=63n/100
so,
m+n= 63n/100 + n
= 163n/100
= 1.63n
ANSWER:C
Answer: (C) 1.63n
Question: In the faculty of Reverse-Engineering, 200 second year students study numeric methods, 400 second year students study automatic control of airborne vehicles and 100 second year students study them both. How many students are there in the faculty if the second year students are approximately 60% of the total?
(A) 834
(B) 750
(C) 633
(D) 654
(E) 812
Rationale: Total number of students studying both are 400 + 200 - 100 = 500 (Subtracting the 100 since they were included in the both the other numbers already).
So 60% of total is 500, so 100% is approx. 834.
Answer is A
Answer: (A) 834
Question: Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 180 feet in circumference.After how many minutes are the three of them together again?
(A) 3 mins
(B) 10 mins
(C) 15 mins
(D) 3 mins
(E) 7 mins
Rationale: Answer will be A.
The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 3 mins.
Answer: (A) 3 mins
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?
(A) 1/26
(B) 1/20
(C) 1/25
(D) 1/29
(E) 1/23
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26.Answer: A
Answer: (A) 1/26
Question: Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 40% in the following week, and increased by 30% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?
(A) 0.875G
(B) 0.9G
(C) 0.925G
(D) 0.95G
(E) 0.975G
Rationale: After 3 weeks, the price was 1.3*0.6*1.25*G=0.975G
The answer is E.
Answer: (E) 0.975G
Question: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 25th in an arithmetic progression if the sum of the 11th and 15th terms of the sequence is 96?
(A) 48
(B) 63
(C) 55
(D) 96
(E) 108
Rationale: Let x be the difference between any two consecutive terms.
The mean of a sequence like this is the middle term, thus the 13th term in the sequence.
Then the mean of the 12th and 14th term is also equal to the overall mean, because the 12th term is (13th term - x) and the 14th term is (13th term + x).
Similarly the mean of the 11th and 15th term is also equal to the mean.
etc...
Thus the mean is 96/2 = 48
The answer is A.
Answer: (A) 48
Question: A train running at the speed of 90 km/hr crosses a pole in 10 seconds. Find the length of the train.
(A) 150
(B) 180
(C) 250
(D) 200
(E) 225
Rationale: Speed = 90*(5/18) m/sec = 25 m/sec
Length of Train (Distance) = Speed * Time
25 *10 = 250 meter
Answer:C
Answer: (C) 250
Question: Exactly two sides of a certain 10-sided die are red. What is the probability that Kumar rolls the die 2 times and the die lands with a red side up for the first time on the second roll?
(A) 0.16
(B) 0.2
(C) 0.3
(D) 0.32
(E) 0.56
Rationale: Total no. of sides = 10
Sides that are red = 2
Probability that the die lands with red side up = 2/10
Therefore, Probability that the die does not land with red side up = 1 - 2/10 = 8/10
Probability that Kumar rolls the die 2 times and the die lands with a red side up for the first time on the second roll
= (1st roll - non red face) X (2nd roll - red face)
= 8/10 x2/10
= 16/100
=0.16
= 0.128
A
Answer: (A) 0.16
Question: The average salary per head of the entire staff of an college including the lecturer and professors is Rs.90. The average salary of professors is Rs.600 and that of the lecturer is Rs.84. If the number of professors is 2, find the number of professors in the office?
(A) 900
(B) 1000
(C) 1020
(D) 1200
(E) 1240
Rationale: 1->12
85->1020
C
Answer: (C) 1020
Question: A lawn is in the form of a rectangle having its sides in the ratio 2: 3. The
area of the lawn is (1/6) hectares. Find breadth of the lawn.
(A) 15 m
(B) 20 m
(C) 25 m
(D) 35 m
(E) 50 m
Rationale: Let length = 2x metres and breadth = 3x metre.
Now, area = (1/6 )x 1000 m2 = 5000/3m2
So, 2x * 3x = 5000/3 <=>x2= 2500/9 <=>x = 50/3
therefore Breadth = 3x = 3(50/3) m
= 50m.
ANSWER E 50 m
Answer: (E) 50 m
Question: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?
(A) 2 years
(B) 7 years
(C) 9 years
(D) 5 years
(E) 3 years
Rationale: Amount = (30000 + 4347) = Rs. 34347
Let the time be n years. Then,
30000(1 + 7/100)n = 34347
= (107/100)n = 34347/30000 = (107/100)2
n = 2 years.
Answer: A
Answer: (A) 2 years
Question: In how many years will a sum of money doubles itself at 5% per annum simple interest
(A) 25 years
(B) 28 years
(C) 10 years
(D) 20 years
(E) 21 years
Rationale: let the initial sum be x
then,Amount=2x(because sum will be double)
Amount = Principal + S.I
2x = x + s.I
S.I = x
S.I = (p*r*t)/100
x = (x*5*t)/100
therefore,t = 20 years
ANSWER:D
Answer: (D) 20 years
Question: An equity analyst needs to select 5 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 10, in how many ways can she choose and rank her top 5 picks?
(A) 21548
(B) 31502
(C) 21250
(D) 30240
(E) 84045
Rationale: Number of ways of choosing 5 stocks = 10C5
Number of ways of ranking the chosen stocks = 5!
Hence total ways of chosing and ranking = 10C5 * 5! = 30240
Correct Option: D
Answer: (D) 30240
Question: A man walking at the rate of 6 km/hr crosses a bridge in 15 minutes. The length of the bridge is ______.
(A) 1000 m
(B) 1250 m
(C) 1500 m
(D) 1800 m
(E) 2300 m
Rationale: Hint: To find the answer in meter, we will first convert distance from km/hour to meter/sec by multiplying it with 5/18 .Also, change 15 minutes to seconds by multiplying it with 60.
Distance = Speed x Time
1. Convert speed into m/sec:
6 x	5 / 18 m/s = 1.66 m/s
2. Convert time from minutes into seconds = 15 x 60 s = 900 sec
3. Calculate : Distance = 1.66 x 900 = 1500 m
ANSWER IS C
Answer: (C) 1500 m
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 7 kmph
(C) 2 kmph
(D) 4 kmph
(E) 6 kmph
Rationale: Explanation:
DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: Option A
Answer: (A) 1 kmph
Question: If 70 percent of the members of a certain organization are women and 7/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization.
(A) I
(B) I,II
(C) III
(D) II
(E) I,II & III
Rationale: 7/10 (70%) of the members are women and 7/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are:
7/10*80 = 56 women;
80 - 56= 24 men;
7/8*24 = 21 married men;
24 - 21 = 3 unmarried men.
So, option I,II is true.
Answer: B
Answer: (B) I,II
Question: A certain deck of cards contains 2 black cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not black?
(A) 15/28
(B) 1/4
(C) 9/16
(D) 1/32
(E) 1/16
Rationale: The question asks they will both be not black. Considering that these are draws without replacement there are following possibilities :
draw 1, draw 2
===== =====
1) Not black, black;
2) black, Not black;
3) black, black;
4) Not black, not black;
The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are black
P(4) = 6/8*5/7=15/28
1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28
A
Answer: (A) 15/28
Question: A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 6.00 a.m., at what time will he first touch a flag at 120 feet from the ground?
(A) 4 p.m.
(B) 5 p.m.
(C) 6 p.m.
(D) 7 p.m.
(E) None of these
Rationale: Explanation:
Net ascent of the monkey in 1 hour = (30 - 20) feet = 10 feet.
So, the monkey ascends 90 feet in 9 hours i.e. till 3 p.m.
Clearly, in the next 1 hour i.e. till 4 p.m. the monkey ascends remaining 30 feet to touch the flag.
Answer:A
Answer: (A) 4 p.m.
Question: A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 18 hours. What is the maximum distance he
can cover?
(A) 20km
(B) 40km
(C) 60km
(D) 80km
(E) 90km
Rationale: t=d/s, so
18=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)
18=x(18/80)
x=80km
ANSWER:D
Answer: (D) 80km
Question: In the exam the average was found to be p mark. After deducting typographical error the average marks of 94 student reduced from 84 to 64 . Due to this the average came down by 18.8 marks. What was the number of students who took the exam?
(A) 100
(B) 120
(C) 110
(D) 130
(E) 160
Rationale: Explanation :
Number of student = (84-64) * 94/18.8 = 100
Answer : A
Answer: (A) 100
Question: A vessel of capacity 2 litre has 25% of alcohol and another vessel of capacity 6 litre had 30% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
(A) 23%.
(B) 71%.
(C) 49%.
(D) 29%.
(E) 51%.
Rationale: 25% of 2 litres = 0.5 litres
30% of 6 litres = 1.8 litres
Therefore, total quantity of alcohol is 2.3 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 23%
ANSWER:A
Answer: (A) 23%.
Question: A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 4 hours. During that time, the faster car traveled 1/3 of the distance XY. How long would it take the slower car to travel the distance XY?
(A) 6 hours
(B) 8 hours
(C) 10 hours
(D) 12 hours
(E) 15 hours
Rationale: If one car travelled 1/3, then the other car must have travelled only 2/3, as they are meeting after 4 hours in a certain point. So:
(2/3)XY= 4*y --> It took the car 4 hours to travel 2/3 of the distance at a constant speed y.
So if we solve this last equation:
2XY= 3*4*y= 6*y --> It will take this car 6 hours in total to reach its final destination.
Answer: A
Answer: (A) 6 hours
Question: If 0.45: x : : 4 : 2, then x is equal to
(A) 0.225
(B) 0.228
(C) 0.254
(D) 0.256
(E) None
Rationale: Sol.
(x×4) = (0.45×2) ⇒ x = 0.9/4 = 0.225.
Answer A
Answer: (A) 0.225
Question: The 480 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT
(A)  4
(B)  20
(C)  30
(D)  40
(E)  90
Rationale: Obviously the number of rows must be a factor of 480. The only option which is not a factor of 480 is E (90).
Answer: E.
Answer: (E)  90
Question: A man on tour travels first 160 km at 56 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
(A) 31.11 km/hr
(B) 35.55 km/hr
(C) 65.9 km/hr
(D) 36 km/hr
(E) 71 km/hr
Rationale: Total time taken = 160/56 + 160/80 = 2720/560 = 34/7 hours
--> Average speed = 320 x 7/34 = 65.9 km/hr.
Answer : C.
Answer: (C) 65.9 km/hr
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 800 m long?
(A) 200 Sec
(B) 190 Sec
(C) 167 Sec
(D) 197 Sec
(E) 179 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 2000 m
T = D/S
T = 2000/10
T = 200 Sec
Answer: A
Answer: (A) 200 Sec
Question: The present population of a town is 3888. Population increase rate is 20% p.a. Find the population of town before 2 years?
(A) 2500
(B) 2100
(C) 3500
(D) 3600
(E) 2700
Rationale: P = 3888
R = 20%
Required population of town = P/(1 + R/100)^T
= 3888/(1 + 20/100)^2
= 3888/(6/5)^2
= 2700(approximately)
Answer is E
Answer: (E) 2700
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
(A) 25 days
(B) 24
(C) 22 days
(D) 27 days
(E) 21 days
Rationale: B
24 days
B = 1/8 – 1/2 = 1/24 => 24 days
Answer: (B) 24
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
(A) 33 1/7 %
(B) 33 9/3 %
(C) 33 1/3 %
(D) 39 1/3 %
(E) 23 1/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer:C
Answer: (C) 33 1/3 %
Question: if price of t.v set is reduced by 18%, then its sale increases by 72%, find net effect on sale value
(A) 41
(B) 45
(C) 46
(D) 47
(E) 48
Rationale: - a + b + ((-a)(b)/100)
= -18+72+(-18*72)/100
= -18+72-13
=41
ANSWER:A
Answer: (A) 41
Question: If g, h, and i are each equal to 1 or 0, which of the following options will not be a correct value for e, given the equation e = g/5 + h/5^2 + i/5^3.
(A) 2/25
(B) 1/5
(C) 1/25
(D) 6/25
(E) 6/125
Rationale: e = g/5 + h/5^2 + i/5^3
= g/5 + h/25+ i/125
= (25g + 5h + i ) /125
Depending on whether g, h and i take 0 or 1:
substitute 0 or 1 for the different values of g, h and i.
Answer A
Answer: (A) 2/25
Question: If the speed of X meters per second is equivalent to the speed of Y meters per hour, what is Y in terms of X? (1 kilometer=1000 meters)
(A) 15x/18
(B) 3600x
(C) 18x/5
(D) 60x
(E) 3600000x
Rationale: x=y/3600
y = 3600x
Answer : B
Answer: (B) 3600x
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
(A) 2
(B) 1
(C) 3
(D) 23
(E) 9
Rationale: 1056/23 = 45.91
that is 23 * 45 = 1035
Now,
1056 - 1035 = 21
To get completely divided by 23 add 2 to 1056
Ans -A
Answer: (A) 2
Question: A car dealership has 40 cars on the lot, 20% of which are silver. If the dealership receives a new shipment of 80 cars, 50% of which are not silver, what percentage of total number of cars are silver?
(A) 30%
(B) 35%
(C) 40%
(D) 45%
(E) 50%
Rationale: The number of silver cars is 0.2*40 + 0.5*80 = 48
The percentage of cars which are silver is 48/120 = 40%
The answer is C.
Answer: (C) 40%
Question: Of the votes cast on a certain proposal, 68 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)
(A) 300
(B) 340
(C) 380
(D) 420
(E) 460
Rationale: Let x be the total number of votes cast.
0.6x = 0.4x + 68
0.2x = 68
x = 340
The answer is B.
Answer: (B) 340
Question: Using all the letters of the word "LIVE", how many words can be formed, which begin with L and end with E?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 2
Rationale: There are four letters in the given word.
Consider 4 blanks ....
The first blank and last blank must be filled with L and E all the remaining two blanks can be filled with the remaining 2 letters in 2! ways.
The number of words = 2! = 2.
ANSWER:E
Answer: (E) 2
Question: Which of the following is satisfied with |x-4|+|x-3|<5?
(A) 1<x<6
(B) 2<x<5
(C) 2.5<x<4.5
(D) 2.5<x<4
(E) 3<x<4
Rationale: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<5-> |x-4+x-3|<5 -> |2x-7|<5, -5<2x-7<5, 2<2x<12, 1<x<6
Therefore, the answer is A.
Answer: (A) 1<x<6
Question: Susan, Tim, Matt and Kim need to be seated in 4 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
(A) 360
(B) 12
(C) 80
(D) 240
(E) 60
Rationale: Total # of arrangement of 4 people is 4!.
In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).
So, # of arrangements to satisfy the given condition is 4!/2=12.
Answer: B.
Answer: (B) 12
Question: H.C.F of 136, 144 and a third number is 8 and their L.C.M is 2^4 * 3^2 * 17 * 7. The third number is:
(A) 154
(B) 248
(C) 360
(D) 424
(E) 168
Rationale: 136 = 2^3 * 17;
144 = 2^4 * 3^2
H.C.F = 2^3 = 8
Since H.C.F is the product of lowest powers of common factors, so the third number must have (2^3 ) as its factor.
Since L.C.M is the product of highest powers of common prime factors, so the third number must have 3 and 7 as its factors.
Third number = 2^3 * 3 * 7
= 168
ANSWER:E
Answer: (E) 168
Question: Five balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?
(A) 60
(B) 90
(C) 120
(D) 150
(E) 180
Rationale: Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.
For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.
For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.
Total of 90 + 60 = 150 possibilities.
Answer D.
Answer: (D) 150
Question: In a school of 800 students, 44% wear blue shirts, 28% wear red shirts, 10% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?
(A) 120
(B) 132
(C) 144
(D) 156
(E) 168
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
800 * 18/100 = 144
The answer is C.
Answer: (C) 144
Question: If 10 gallons of grape juice are added to 30 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice?
(A) 14%
(B) 25%
(C) 28%
(D) 32.5%
(E) 50%
Rationale: OFFICIAL SOLUTION:
If we start with 40 gallons of a mixture that is 10% grape juice, then we have:
30 × 0.10 = 3 gallons of grape juice.
30 × 0.90 = 27 gallons of other components.
If we add 10 gallons of grape juice, we will end up with 13 gallons of grape juice and 36 gallons of other components, and we will have a total of 40 gallons of the mixture.
So 13/40 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 32,5%.
The correct answer is choice (D)
Answer: (D) 32.5%
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 17 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
(A) 40.3
(B) 40.4
(C) 40.6
(D) 40.8
(E) None of the above
Rationale: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 17 = 403
Hence, new average = 403⁄10 = 40.3
Answer A
Answer: (A) 40.3
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
(A) 400
(B) 500
(C) 600
(D) 20
(E) 25
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e., = 500 ways.
ANSWER:B
Answer: (B) 500
Question: A man gains 40% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be.
(A) 130%
(B) 180%
(C) 150%
(D) 160%
(E) 170%
Rationale: Explanation:
Let the C.P. = x,
Then S.P. = (140/100)x = 7x/5
New S.P. = 2(7x/5) = 14x/5
Profit = 14x/5 - x = 9x/5
Profit% = (Profit/C.P.) * 100
=> (9x/5) * (1/x) * 100 = 180 %
Option B
Answer: (B) 180%
Question: Replace The Asterisk Mark Below With Correct Number ?
2 {38} 3
4 {1524} 5
6 {3548} 7
8 {****} 9
(A) 7291
(B) 6380
(C) 7298
(D) 8332
(E) 3829
Rationale: B
6380
2*2-1 3*3-1 =>38
4*4-1 5*5-1 =>1524 and so on
Answer: (B) 6380