mathewhe/aqua_rat huggingface dataset:
Question: What is the probability for a family with four children to have a boy and three girls (assuming the probability of having a boy or a girl is equal)?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: One possible case is: girl - girl - girl - boy
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
There are 4C3 = 4 such cases so we should multiply by 4.
P(one boy and three girls) = 4/16 = 1/4
The answer is C.
Answer: (C) 1/4
Question: A train 120 m long crosses a platform with a speed of 60 kmph in 15 sec; find the length of the platform?
(A) 110
(B) 130
(C) 120
(D) 125
(E) 135
Rationale: D = 120 + x
T = 15
S = 120+x/15 * 18/5 = 60 kmph.
=> (120+x) * 18 = 4500
=> 120 + x = 250 => x= 130 m
Answer: B
Answer: (B) 130
Question: What is the next number of the following sequence
8,8,15,23,39.....
(A) 44
(B) 54
(C) 64
(D) 74
(E) 68
Rationale: 8,8,15,23,39, x
8 + 8 = 16 ==> 16 - 1 =15
8 + 15 = 23==> 23 + 0 =23
15 + 23 = 38=> 38 + 1 =39
23 + 39 = 62=> 62 + 2 = 64
ANSWER:C
Answer: (C) 64
Question: A recycling facility is staffed by 9 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/9 of all wages paid at the facility, what is the value of n?
(A) 8/7
(B) 8
(C) 9/8
(D) 7
(E) 5
Rationale: Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 9x+xn and we are told that it equals to 9xn:
9x+xn=9xn --> reduce by x: 9+n=9n -->8n=9
n = 9/8
Answer: C
Answer: (C) 9/8
Question: In how many ways a team of 11 must be selected from 5 men and 11 women such that the team must comprise of not more than 3 men?
(A) 2256
(B) 2377
(C) 2797
(D) 2672
(E) 1991
Rationale: Ans: C
Explanation;
The team may consist of 0 men + 11 women, 1 men + 10 women, 2 men + 9 women, or 3 men + 8 women.
So Number of ways are = 11C11+5C1×11C10+5C2×11C9+11C11+5C1×11C10+5C2×11C9+5C3×11C85C3×11C8
= 2256
Answer:A
Answer: (A) 2256
Question: A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is
(A) 600
(B) 750
(C) 1000
(D) 1250
(E) None of these
Rationale: Explanation:
speed = (5 × 5/18)m/sec
= 25/18 m/sec.
Distance covered in 15 minutes = (25/18 × 15 × 60)m
= 1250 m.
Answer: D
Answer: (D) 1250
Question: A division of a company consists of three men and four women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
(A) 1/4
(B) 2/7
(C) 3/11
(D) 4/15
(E) 5/21
Rationale: Total number of ways to select 2 members = 7C2 = 21
Total number of ways to select 2 females = 4C2 = 6
P(two females) = 6/21 = 2/7
The answer is B.
Answer: (B) 2/7
Question: Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
(A) 140
(B) 330
(C) 460
(D) 590
(E) 270
Rationale: Let x be the total number of pages in the book, then she finished 2/3⋅x pages.
Then she has x−2/3⋅x=1/3⋅x pages left.
2/3⋅x−1/3⋅x=90
1/3⋅x=90
x=270
So the book is 270 pages long
correct answer E
Answer: (E) 270
Question: The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that ofthe failed candidates is 15,what is the no. of candidates who passed the examination
(A) 14 years
(B) 14 years 3 month
(C) 14 years 8 month
(D) 15 years 8 month
(E) 16 years 2 month
Rationale: (d) Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
2.(a) Total increase = 8 * 2 = 16 years
So, total age of two women = 35 + 45 +16= 96
Average age of two women=96/2=48 years
3(d) Total decrease = 20 * 2 = 40 month
= 3 years 4 month
So, age of new boy = 18 years – 3 years 4 month
= 14 years 8 month
C
Answer: (C) 14 years 8 month
Question: A clock shows the time as 8 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?
(A) 45 minutes
(B) 55 minutes
(C) 35 minutes
(D) 25 minutes
(E) 50 minutes
Rationale: there are 10 hours in between 8 a.m. to 6 p.m.
10*5=50 minutes.
ANSWER:E
Answer: (E) 50 minutes
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 277
(B) 444
(C) 128
(D) 127
(E) 109
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer:B
Answer: (B) 444
Question: Find the odd man out. 742, 743, 633, 853, 871, 616, 532
(A) 616
(B) 990
(C) 633
(D) 743
(E) None of these
Rationale: Explanation :
In all numbers except 616, the difference of third and first digit is the middle digit. Answer : Option A
Answer: (A) 616
Question: For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 6| + |-b| + |b – a| + |ab| =
(A) ab + 2b + 6
(B) a-b-6
(C) a+b+6
(D) 2a+2b-6
(E) 2a+b+6
Rationale: Observation-1: |a – b| = b – a
which is possible only when signs of a and b are Same
Since Given a > 0
so we figure out that a and b are both positive
Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a
Now you may choose the values of a and b based on above observations
e.g. b = 6 and a=1 and check the value of given functions and options
|a + 6| + |-b| + |b – a| + |ab| = |1 + 6| + |-6| + |6 – 1| + |1*6| = 24
ab + 2b + 6= 1*6+12+6=24
all other options are not equal to 24
Answer : A
Answer: (A) ab + 2b + 6
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
(A) 209
(B) 210
(C) 230
(D) 235
(E) 240
Rationale: Option 'B'
7p3 = 7 × 6 × 5 = 210
Answer: (B) 210
Question: If s and t are positive integers such that s/t = 64.18, which of the following could be the remainder when s is divided by t ?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45
Rationale: The remainder is 0.18 or 18/100. You can go one step further and say that X/Y=18/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.
One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.
45/Y=18/100
18Y=4500
Y=250
Answer: E.
Answer: (E) 45
Question: In a party men drink only beer, women drink only wine , sons drink only orange juice and daughters drink only apple juice. There are 1.05L of beers, 1.05L of wine 3.5L of orange juice and 4.9L of apple juice. If every one has the same drinking capacity then what can be the minimum number of people present at the party?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Take HCF of 1.05,1.05,3.5,4.9.
which is 0.35.
Then divide each quantity by HCF to get the number people drinking that particular beverage.
i.e 3+3+10+14=30.
ANSWER:B
Answer: (B) 30
Question: Which is a better investment 6% stock at of 220 or 5 1/2 stock at 200?
(A) 6% stock at of 220
(B) Cannot be compared, as the total amount of investment is not given
(C) Both are equally good
(D) None
(E) 5 1/2 stock at 200
Rationale: Let investment in each case be Rs. (220 x 200).
Income in 1st case = Rs.6 x 220 x 200/220	= Rs. 1200.
Income in 2nd case = Rs.11 x 220 x 200/(2*200)= Rs. 1210
Clearly, 5 1/2 stock at 200 is better.
ANSWER:E
Answer: (E) 5 1/2 stock at 200
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 30 sec respectively. What is the speed of the train?
(A) 89
(B) 23
(C) 56
(D) 43.2
(E) 67
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/30 = y
y = 12
Speed = 12 m/sec = 12 * 18/5 = 43.2 km/hr.
Answer: Option D
Answer: (D) 43.2
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
(A) 4800
(B) none of these
(C) 3600
(D) 1200
(E) 2400
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
Answer is E.
Answer: (E) 2400
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
(A) 24
(B) 18
(C) 20
(D) 25
(E) 16
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
ANSWER B
Answer: (B) 18
Question: Amol was asked to calculate Arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged the 2 digits, say a and b,in one of these 10 integers. As a result, his answer for the Arithmetic mean was 1.8 more than what it should have been. Then b - a equals
(A) 1
(B) 2
(C) 3
(D) 4
(E) None of these
Rationale: Explanation :
Arithmetic mean is more by 1.8 means sum is more by 18.
So, ba – ab = 18.
b > a because sum has gone up, e.g. 31 – 13 = 18.
Hence, b – a = 2.
Answer : B
Answer: (B) 2
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.24000. A's share is?
(A) 2999
(B) 8000
(C) 6000
(D) 2889
(E) 6612
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 24000 = 8000
Answer:B
Answer: (B) 8000
Question: From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 15 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009?
(A) 80
(B) 103.5
(C) 95
(D) 100
(E) 108
Rationale: Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 20% = 90*1.15 = 103.5
Thus ratio = 103.5/100 = 1.03 (in % terms = 103%). Thus B is the correct answer.
Answer: (B) 103.5
Question: A man’s speed with the current is 16 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
(A) 8.5 km/hr
(B) 9.5 km/hr
(C) 11 km/hr
(D) 12.5 km/hr
(E) None of these
Rationale: Solution
Man's rate in still water = (16-2.5) km/hr = 13.5 km/hr.
Man's rate against the current = (13.5-2.5) km/hr = 11 km/hr Answer C
Answer: (C) 11 km/hr
Question: A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
(A) 250
(B) 350
(C) 450
(D) 550
(E) 650
Rationale: The number of chocolate bars is equal to
18 * 25 = 450
correct answer C
Answer: (C) 450
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 11
(B) 50
(C) 99
(D) 77
(E) 55
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: B
Answer: (B) 50
Question: A boy has 10 trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 120ways
(B) 110ways
(C) 125ways
(D) 130ways
(E) 145ways
Rationale: The boy can select one trouser in 10 ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 10 * 12
= 120 ways.
Answer: A
Answer: (A) 120ways
Question: A bag contains 6 red, 4 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 1/13
(B) 2/23
(C) 5/26
(D) 5/22
(E) 3/23
Rationale: P(Both are red),
=6C212C2=6C212C2
=15/66=5/22
D
Answer: (D) 5/22
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
(A) Remains same
(B) 5% decrease
(C) 5% increase
(D) 10% increase
(E) 20% increase
Rationale: 100 * 100 = 10000
125 * 80 = 10000
No change
ANSWER:A
Answer: (A) Remains same
Question: From the word 'ASTOUNDER', how many independent words can be made with-out changing the order of the letters and using each letter only once ?
(A) 5
(B) 8
(C) 3
(D) 2
(E) 9
Rationale: Explanation:
The words formed are
AT and UNDER, AS and UNDER (or) AT and SOUND
Answer: D) 2
Answer: (D) 2
Question: If each side of a square is increased by 25%, find the percentage change in its area.
(A) 26.25%
(B) 36.25%
(C) 46.25%
(D) 56.25%
(E) 66.25%
Rationale: Let each side of the square be a. Then, area = a2.
New side =(125a/100) =(5a/4). New area = (5a/4) 2=(25a2)/16.
Increase in area = ((25 a2)/16)-a2=(9a2)/16.
Increase% = [((9a2)/16)*(1/a2)*100] % = 56.25%.
Option D
Answer: (D) 56.25%
Question: Two persons starting from the same place walk at a rate of 10kmph and 14.5kmph respectively. What time will they take to be 18km apart, if they walk in the same direction?
(A) 4 hrs
(B) 9 hrs
(C) 5 hrs
(D) 2 hrs
(E) 6 hrs
Rationale: The relative speed of the boys = 14.5kmph – 10kmph
= 4.5 kmph
Distance between them is 18 km
Time= 18km / 4.5 kmph = 4 hrs
Answer : A
Answer: (A) 4 hrs
Question: Three partners A,B and C invest Rs.18000, Rs.22500 and Rs.27000 respectively in a business. If total profit is Rs.12000 then B's share is (in Rs.)
(A) 10000
(B) 6500
(C) 4000
(D) 7500
(E) 8500
Rationale: 18000:22500:27000
4:5:6
B's share=12000*5/15=4000
ANSWER:C
Answer: (C) 4000
Question: The school soccer team looks at their record and finds that they win, lose, and tie games in a ratio of 4:3:1. How many games did they play if they lost 9 games?
(A) 3
(B) 9
(C) 12
(D) 18
(E) 24
Rationale: The ratio is 4 wins: 3 losses: 1 tie.
Think of ratio as "parts."
Divide 9 (total losses) by 3 (ratio losses) to find 1 "part" of the ratio.
9/3 = 3
This means the team tied 3 games.
Multiply 3 (1 "part" of ratio) by 4 (ratio wins) to find total wins.
3*4 = 12.
This mean the team won 12 games.
Add up wins, losses, and ties.
12+9+3 = 24
The answer is E
Answer: (E) 24
Question: A gardener wants to plant trees in his garden in rows in such a way that the number of trees in each row to be the same. If there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row?
(A) 63
(B) 28
(C) 48
(D) 32
(E) 33
Rationale: Required number of trees
= 24/36 * 42 = 28.
ANSWER:B
Answer: (B) 28
Question: What is the average of xx, 2x2x, and 66?
(A) x+2x
(B) 2x+2
(C) x+2x+2
(D) 2x
(E) 2x+1
Rationale: By the definition of an average, we get:
x+2x+63=3x+63x+2x+63=3x+63
=3(x+2)3=x+2.=3(x+2)3=x+2.
Hence, the answer is x+2x+2 or Option C
Answer: (C) x+2x+2
Question: Five fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 6
(B) 8
(C) 12
(D) 16
(E) 20
Rationale: 5*4 = 20
The answer is E.
Answer: (E) 20
Question: In the city of San Durango, 80 people own cats, dogs, or rabbits. If 50 people owned cats, 20 owned dogs, 30 owned rabbits, and 16 owned exactly two of the three types of pet, how many people owned all three?
(A) 1
(B) 2
(C) 4
(D) 7
(E) 9
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
80 = 50 + 20 + 30 - (16) - 2x
x = 2
So, answer will be B
Answer: (B) 2
Question: If 20% of a = b, then b% of 20 is the same as:
(A) None of these
(B) 10% of a
(C) 4% of a
(D) 20% of a
(E) 30% of a
Rationale: Explanation:
20% of a=b
b=20a/100=a/5
b% of 20=20 x b/100
=b/5=a/5x1/5=a/25
=4a/100=4% of a
ANSWER IS C
Answer: (C) 4% of a
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/91%
(B) 18 2/11%
(C) 18 9/11%
(D) 18 2/91%
(E) 12 2/11%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer:B
Answer: (B) 18 2/11%
Question: The cost of 12 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?
(A) Rs 52.50
(B) Rs 56
(C) Rs 58.50
(D) Rs 70
(E) None of these
Rationale: Explanation :
Let the required cost be Rs. x. Then,
More packets, More cost (Direct Proportion)
More weight, More cost (Direct Proportion)
Packets 12 : 27
Weight 900 : 1000 :: 28 : x
(12 x 900 x x) = (27 x 1000 x 28)
x = (27 x 1000 x 28) /12 x 900
=70
Answer D
Answer: (D) Rs 70
Question: A train 490 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 15 sec
(B) 16 sec
(C) 28 sec
(D) 20 sec
(E) 25 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 490 * 2/35 = 28 sec
ANSWER: C
Answer: (C) 28 sec
Question: Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship?
? : 4623 :: 9 : 647
(A) 17
(B) 16
(C) 14
(D) 19
(E) 20
Rationale: E
17
Explanation :
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647
Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623
Answer: (E) 20
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 60 years now, the son's age 10 years back was?
(A) 12yr
(B) 15yr
(C) 14yr
(D) 10yr
(E) 20yr
Rationale: Let the son's present age be x years
Then, 60-x = x
x = 30
Son's age 10 years back = 30-10 = 20years
Answer is E
Answer: (E) 20yr
Question: A coin is tossed 3 times. Find out the number of possible outcomes.
(A) None of these
(B) 8
(C) 2
(D) 1
(E) 3
Rationale: Explanation :
When a coin is tossed once, there are two possible outcomes - Head(H) and Tale(T)
Hence, when a coin is tossed 3 times, the number of possible outcomes
= 2 x 2 x 2 = 8
(The possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT ) Answer : Option B
Answer: (B) 8
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 3.5%
(B) 4.5%
(C) 5.6%
(D) 6.5%
(E) 2.5%
Rationale: Cost Price of 1 toy = Rs.375/12= Rs. 31.25
Selling Price of 1 toy = Rs. 33
So, Gain = Rs. (33 - 31.25) = Rs. 1.75
Profit % =(1.75/31.25x 100)%	=28/5% =5.6%
Answer is C.
Answer: (C) 5.6%
Question: A box contains 2 white balls, 3 black ball and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
(A) 74
(B) 58
(C) 12
(D) 52
(E) 64
Rationale: We may have ( 1 black and 2 non black) or (2 black and 1 non black)or(3 black)
=3c1 x 6c2 + 3c2 x 6c1 +3c3
=64
ANS: E
Answer: (E) 64
Question: What is the remainder when 8^381 is divided by 5 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: I also agree that the remainder is '3' (using the last digit of the powers of 7). Could we have the official answer please?D
Answer: (D) 3
Question: The average of seven consecutive numbers A, B, C, D, E, F and G is 9. What percent of G is A?
(A) 42.0
(B) 48.0
(C) 50.0
(D) 52.2
(E) 54.0
Rationale: Explanation :
In such a case the middle number (D) is the average
∴ D = 9 and A = 6 and G = 12
Required percentage = 6/12 x 100 = 50.0
Answer : Option C
Answer: (C) 50.0
Question: A baker charges N dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: We're told that by selling cakes at N dollars/cake, a baker will make $320.
Reducing the price by 20% and selling 2 MORE cakes will also make her $320.
We're asked for the original number of cakes that the baker intends to sell.
$320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....
Let's TEST ANSWER D: 8 cakes
IF....
Original cakes = 8
8(N) = $320, so N = $40/cake
20% off = $8 off = 40-8 = $32/cake
+2 more cakes = 8+2 = 10 cakes
10(32) = $320
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
D
Answer: (D) 8
Question: If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC?
(A) 9
(B) 18−3√3
(C) 18
(D) 18+3√3
(E) 27
Rationale: The altitude of an equilateral triangle is side*√3/2.
As perimeter of triangle ACD is 9+3√3, AC + CD + AD =
(side+side/2+side*√3/2) = 9 + 3√3 or side =6.
Perimeter of equilateral triangle, ABC is 3(side) or 18.
Answer:(OptionC)
Answer: (C) 18
Question: We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $396. How many math books did we buy?
(A) 47
(B) 54
(C) 56
(D) 61
(E) 64
Rationale: M + H = 90
H = 90 - M
4M + 5H = 396
4M + 5*(90 - M) = 396
M = 54
The answer is B.
Answer: (B) 54
Question: Kamalesh worked 27days and completed 75 percent of a particular work. Then he took the help of Lucifer and they together completed the remaining work in 5 days. How long will Lucifer take to complete the same work,if he is working alone
(A) 10 DAYS
(B) 40 DAYS
(C) 45 DAYS
(D) 47 DAYS
(E) 49 DAYS
Rationale: Kamlesh completed 75% of the work in 27 days. So,
Work rate of Kamlesh = 75/27 = 2.775 per day.
Kamlesh and Lucifer complted 25% remaining work in 5 days.Then
Work rate of Kamlesh and Lucifer, together = 25/5 = 5% per day.
So, Work rate of Lucifer = 5 - 2.77 = 2.23% per day.
To complete 100% work alone, Lucifer needs,
= 100/2.23 = 45 days.
ANSWER : OPTION C
Answer: (C) 45 DAYS
Question: Find out the wrong number in the series.
6, 12, 48, 98, 384, 768, 3072
(A) 768
(B) 384
(C) 98
(D) 488
(E) 12
Rationale: Each even term of the series is obtained by multiplying the previous term by 2.
2nd term = (1st term) x 2 = 6 x 2 = 12
4th term = (3rd term) x 2 = 48 x 2 = 96.
6th term = (5th term) x 2 = 384 x 2 =768.
4th term should be 96 instead of 98.
ANSWER:C
Answer: (C) 98
Question: Two friends plan to walk along a 36-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 25% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other?
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: If Q complete x kilometers, then P completes 1.25x kilometers.
x + 1.25x = 36
2.25x=36
x = 16
Then P will have have walked 1.25*16=20 km.
The answer is B.
Answer: (B) 20
Question: The ratio of boys to girls in Class A is 3 to 5. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Since it is given that the ratio of boys to girls in Class A is 3 to 4 - so we can quickly eliminate the answer choices which are not multiples of 4.
so ans can either be 8 0r 12.
With 8 as answer - no of girls = 8
With 12 as answer - no of girls = 12
Now Class A has one more boy and two more girls than class B and also the ratio of boys to girls in Class B is 4 to 5.
So we are looking for number of girls in B to be divisible by 5.
With 8 as answer -> Girls = 8-2 = 6. (Not possible)
With 12 as answer -> Girls = 12-2 = 5.
So, answer = 10. ( C)
Answer: (C) 10
Question: A man has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 45
(B) 60
(C) 75
(D) 90
(E) 105
Rationale: Answer : B
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 320
16x = 320
x = 20.
Hence, total number of notes = 3x = 60.
Answer: (B) 60