mathewhe/aqua_rat huggingface dataset:
Question: In a games hour 4 different types of players came to the ground? cricket 18, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 5 people play both cricket and football. How many people play only cricket?
(A) 11
(B) 9
(C) 5
(D) 3
(E) 9
Rationale: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.
people play only cricket = 18-4-5 = 9
Answer is B
Answer: (B) 9
Question: The average weight of A,B,C is 45 Kg. The avg wgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.
(A) 36kg
(B) 84kg
(C) 31kg
(D) 45kg
(E) 12kg
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.
Ans: B
Answer: (B) 84kg
Question: Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 0 through 8 appears in one of these three integers, what is the maximum possible value of the sum of a, b, and c?
(A) 2233
(B) 2774
(C) 2223
(D) 2345
(E) 2135
Rationale: According to the stem we should use the digits 0 through 7 to construct 3 three-digit integers, so that their sum is as large as possible.
To maximize the sum, maximize the hundreds digits of a, b, and c, so make them 8, 7, and 6.
Next, minimize tens digits. Make them 5, 4, and 3.
Use the remaining digits (2, 1, and 0) for units digits.
So, a would be 852, b would be 741 and c would be 630.
741 + 852 + 630 = 2223.
Answer: C.
Answer: (C) 2223
Question: In a certain city , there are two football teams , 65 percent of the people prefer team (A) and the rest prefer team (B),
Team (A) is going to play against team (C) from another city. If 80 percent of people who prefer team (A) are going to attend the match , and 20 percent of the people who prefer team (B) are going to attend the match , what percent of city's people are going to attend the match ?
(A)  45%
(B)  59%
(C)  60%
(D)  61%
(E)  68%
Rationale: say the population of the city is 100 person , so there are 65 persons prefer team (A) and 35 persons prefer team(B) .
65*0.8=52 person who prefer team (A) are going to attend the match
35*0.2=7 person who prefer team (B) are going to attend the match
Thus total of 52+7=59 persons are going to attend the match , which is 59 percent of population.
answer: B
Answer: (B)  59%
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 25 hours and 16 hours respectively. The ratio of their speeds is
(A) 4:1
(B) 4:2
(C) 4:5
(D) 4:3
(E) 4:6
Rationale: Ratio of their speeds = Speed of first train : Speed of second train
= √16−−√25
= 4:5
Answer is C
Answer: (C) 4:5
Question: In an election between two candidates first candidate got 60% of votes polled and second Candidate got 250 votes. The total number of votes polled was?
(A) votes
(B) votes
(C) votes
(D) votes
(E) votes
Rationale: Total = 100 %,
First person got 60%
second person got remaining 40 % of votes.
than 40 % = 250
40% = 40×7 = 250
100% =100×7 =700 votes
A)
Answer: (A) votes
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (8, 0), (0, -3.5), (-8, 0)?
(A) 56
(B) 88
(C) 112
(D) 116
(E) 120
Rationale: Area of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 8+8= 16
Length of 2nd diagonal= 3.5+3.5= 7
Area= 1/2*16*7= 56
A is the answer
Answer: (A) 56
Question: The value of Underrot 130pi/4 + Underrot 1 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question)
(A) 108
(B) 114
(C) 125
(D) 120
(E) 103
Rationale: Under root (130pi/4) ~ 102
Under root (1) = 1
Hence, 102+1 = 103 is the approx answer. E is the correct answer.
Answer: (E) 103
Question: A train crosses a platform of 100 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150
(B) 88
(C) 77
(D) 62
(E) 350
Rationale: Length of the train be â€˜Xâ€™
X + 100/15 = X + 250/20
4X + 400 = 3X + 750
X = 350m
Answer: E
Answer: (E) 350
Question: What is the 20th digit to the right of the decimal point in the decimal expansion of 1/37?
(A)  0
(B)  2
(C)  4
(D)  7
(E)  9
Rationale: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (2nd, 4th, 6th, ...) to the right of the decimal point is alternating by 2, 0, 7 thus 20th digit is 2.
Answer: B.
Answer: (B)  2
Question: In a six-sided polygon XQRSTV ∠X measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠X equal to, in degrees?
(A)  72
(B)  80
(C)  88
(D)  96
(E)  104
Rationale: The sum of interior angle in a polygon is (n-2)*180
so for a six sided figure, (6-2)*180 = 720
let the A.M of the other 5 angles be 'm'
--> m*5 + ∠X = 720, we know ∠X=m-48
--> m*5 + m - 48 = 720, solving we get m=128
hence ∠X= 128-48 = 80
Ans B.
Answer: (B)  80
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1:2
(B) 2:1
(C) 1:3
(D) 3:1
(E) 1:1
Rationale: Explanation:
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:30000×9
=45×12:30×9
=3×12:2×9
=2:1
Answer: Option B
Answer: (B) 2:1
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
(A) 34 sec
(B) 11 sec
(C) 12 sec
(D) 10 sec
(E) 15 sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
Answer:D
Answer: (D) 10 sec
Question: 150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?
(A) 16
(B) 60
(C) 66
(D) 52
(E) 51
Rationale: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = 7x/30 kg.
Quantity consumed by 70 men in x days = (7x/30)(70)kg
(7x/30)(70) = 980
x = (980 * 30)/490 => x = 60 days
Answer:B
Answer: (B) 60
Question: A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 4 miles per day and it will take them two days, how many miles long is the route down the mountain?
(A) 4
(B) 6
(C) 8
(D) 12
(E) 16
Rationale: D = S*T
Given condition is for UP the mountain hikers takes 4 miles per day and total 2 days... miles = 8 miles...
For DOWN speed they take = 3/2(4) = 6 miles per day and for the same 2 days... miles = 12 miles..
Answer: option D is correct answer
Answer: (D) 12
Question: The ratio of three numbers is 3:4:7 and their product is 18144. The numbers are
(A) 9,12,21
(B) 15,20,25
(C) 18,24,42
(D) 24,15,17
(E) 30,12,7
Rationale: Let the numbers be 3x, 4x and 7x
3x x 4x x 7x=18144
X3=216
X=6
The numbers are 18,24,42
ANSWER C 18,24,42
Answer: (C) 18,24,42
Question: If the radius of a circle is increased by 30% then the area is increased by:
(A) 44%
(B) 69%
(C) 144%
(D) 40%
(E) None of the above
Rationale: initially A=pi*r2
now R2=130/100r
then area=Pi*(130R/100)2
area=169R/100
that is area increases from 100 to 169=increase in area=69%
ANSWER:B
Answer: (B) 69%
Question: Angelina walked 1200 meters from her home to the grocery at a constant speed. She then walked 480 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
(A) 12
(B) 23
(C) 34
(D) 48
(E) 52
Rationale: let the speed be X...
so time taken from home to grocery= 1200/x..
the speed to gym = 2x..
so time taken = 480/2x=240/x..
its given 1200/x-240/x=40..
960/x=40..
x=24m/secs..
so grocery to gym=2*24=48m/s...
D
Answer: (D) 48
Question: A set of pictures of butterflies contains 10 pictures. Jim bought 3 of the pictures. If 2 pictures are to be picked out from the 10 pictures, what is the probability that both pictures are not those that were already bought by Jim?
(A) 14/15
(B) 3/5
(C) 6/13
(D) 7/15
(E) 7/10
Rationale: Probability of first pick not one of the Jim's picture is = 7/10 (except for 3 which Jim purchased)
Probability of second pick not one of the Jim's picture is = 6/9
Total = 7/10∗6/9=7/15
Answer is D
Option D
Answer: (D) 7/15
Question: What least number must be added to 1096, so that the sum is completely divisible by 23 ?
(A) 2
(B) 1
(C) 3
(D) 5
(E) 8
Rationale: 1096/23 = 47.6--
that is 23 * 47 = 1081
Now,
1096- 1081 = 15
To get completely divided by 23 add 8 to 1096
Ans -E
Answer: (E) 8
Question: The sum of the present ages of two persons A and B is 45. If the age of A is twice that of B, find the sum of their ages 5 years hence?
(A) 55
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: A + B = 45, A = 2B
2B + B = 45 => B = 15 then A = 30.
5 years, their ages will be 35 and 20.
Sum of their ages = 35 + 20 = 55.
ANSWER:A
Answer: (A) 55
Question: How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?
(A) 40
(B) 400
(C) 5040
(D) 2520
(E) None of these
Rationale: Solution
'LOGARITHM' contain 10 different letters.
Required number of words = Number of Arrangement of 10 letters, taking 4 at a time
= 10 P 4 = (10 × 9 × 7) = 5040 . Answer C
Answer: (C) 5040
Question: The average monthly income of A and B is Rs. 4050. The average monthly income of B and C is Rs. 5250 and the average monthly income of A and C is Rs. 4200. What is the monthly income of A?
(A) 2000
(B) 2500
(C) 3000
(D) 3500
(E) 4000
Rationale: Let monthly income of A = x
monthly income of B = y
monthly income of C = z
x + y = 2 × 4050 .... (Equation 1)
y + z = 2 × 5250 .... (Equation 2)
z + x = 2 × 4200 .... (Equation 3)
(Equation 1) + (Equation 3) - (Equation 2)
=> x +y + x + z - (y + z) = (2 × 4050) + (2 × 4200) - (2 × 5250)
=> 2x = 2(4050 + 4200 - 5250)
=> x = 3000
i.e., Monthly income of A = 3000
ANSWER:C
Answer: (C) 3000
Question: Which of the following is a divisible by 3 number ?
(A) 10000
(B) 20000
(C) 30000
(D) 40000
(E) 50000
Rationale: Explanation :
C is divisible by 3 with out integers.
Answer : Option C
Answer: (C) 30000
Question: If 11 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A)  10•9•8•7•6•5•4•3•2•1
(B)  10•10
(C)  55
(D)  45
(E)  36
Rationale: We got #11 people who shake each other's hands once ==> a pair of 2
11!/9!2! = 11*10 / 2*1 = 55.
Hence answer C.
Answer: (C)  55
Question: A zinc-copper alloy with 5 kg of pure zinc would contain 90% of zinc. The alloy with 3 kg of 90% zinc alloy contains 84% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.
(A) 2.4 kg or 80%
(B) 1.4 kg or 88%
(C) 4.3 kg or 60%
(D) 7.4 kg or 18%
(E) 1.4 kg or 60%
Rationale: Right Answer Explanation:
x : 5
y : 100
90
10 : 90 – y
(90-y)/5 = 10/x = ………..(1)
In the second case,
x 3
y 90
84
6 84-y
Therefore (84-y)/3 = 6/x ………..(2)
Dividing (1) and (2)
=
810 – 9y = 2100 – 25y
16y = 1290
y = 80.625
x = 50/(90-80.625) = 50/9.375 = 5.33 kg
Quantity of zinc in x = 80.625% of x
= 0.80625 5.33
= 4.3 kg
Weight and percentage of zinc is 4.3 kg or 80.625%
C
Answer: (C) 4.3 kg or 60%
Question: If the charge of staying in a student youth hostel $18.00/day for the first week, and $12.00/day for each additional week, How much does it cost to stay for 23 days?
(A) $318
(B) $289
(C) $282
(D) $274
(E) $286
Rationale: Total number of days of stay = 23
Charge of staying in first week = 18*7 = 126 $
Charge of staying for additional days =(23-7)*12 = 16*12 = 192 $
Total charge =126 +192 = 318$
Answer A
Answer: (A) $318
Question: If one root of the equation 2x^2 + 3x – k = 0 is 7, what is the value of k?
(A) 100
(B) 110
(C) 119
(D) 120
(E) 112
Rationale: We just enter this root into the equation in order to recieve an equation to find the answer!
2*7^2+3*7-k=0
k=98+21=119
The answer is C
Answer: (C) 119
Question: Two trains running in opposite directions cross a pole placed on the platform in 47 seconds and 31 seconds respectively. If they cross each other in 33 seconds, what is the ratio of their speeds?
(A) 1:7
(B) 8:7
(C) 6:7
(D) 6: 5
(E) 4:7
Rationale: Explanation:
Let the speed of the trains be x and y respectively
length of train1 = 47x
length of train2 = 31y
Relative speed= x + y
Time taken to cross each other = 33 s
=> = 33
=> (47x + 31 y) = 33(x + y)
=> 14x = 2y
=> x/y = 2/14 = 1/7
= 1:7
Answer: A
Answer: (A) 1:7
Question: If an object travels 400 feet in 4 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
(A) 68
(B) 54
(C) 87
(D) 96
(E) 15
Rationale: 1 mile = 5280 feet
=> 1 feet = 1/5280 miles
If the object travels 400 feet in 4 sec
then it travels 400/4 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)
= 3600 * 100 feet in 1 hour
= 360000 feet in 1 hr
= 360000/5280 miles in 1 hour
= 36000/528 miles/hr ~ 68 miles/hr
Answer - A
Answer: (A) 68
Question: How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?
(A) 3387
(B) 2888
(C) 2788
(D) 1200
(E) 2881
Rationale: 50/100 * x = 30 * 20 => x
= 1200
Answer: D
Answer: (D) 1200
Question: In an organisation there are 1000 employees out of which 250 earn below 10k$ and 500 earn between 10k$ and 50k$. What is the total percentage of employees who earn less than 50k$?
(A) 66%
(B) 75%
(C) 70%
(D) 50%
(E) 82%
Rationale: total percentage = (250+500)/1000 = 0.75
B
Answer: (B) 75%
Question: What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
(A) 9
(B) 5
(C) 2
(D) 7
(E) 1
Rationale: Explanation:
6)4456(742
42
--------
25
24
-------
16
12
-----
4
------
Required number = (6-4) = 2.
Answer: C) 2
Answer: (C) 2
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs.529 is required to paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
(A) 12
(B) 18
(C) 20
(D) 22
(E) 23
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 529/3 = 176.33 sq m
l b = 176.33 i.e., l * l/3 = 176.33
l^2 = 529 => l =23
E
Answer: (E) 23
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 500 m long?
(A) 266 Sec
(B) 170 Sec
(C) 776 Sec
(D) 166 Sec
(E) 997 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1700 m
T = D/S
T = 1700/10
T = 170 Sec
Answer: B
Answer: (B) 170 Sec
Question: The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits when the jacket is laid on a flat surface. The American size of a suit jacket is P inches, where P is twice the linear distance between the armpits when the jacket is laid on a flat surface. If, for a particular jacket, N = P + 16, which of the following is closest to the value of N? (One inch is approximately 2.54 centimeters.)
(A) 36
(B) 47
(C) 58
(D) 65
(E) 72
Rationale: Since one inch is approximately 2.54 centimeters, then N centimeters is N/2.54 inches.
Next, since the American size (P inches) is twice the Italian size (N/2.54 inches), then P=2*N/2.54.
As given that N = P + 16, then N=2*N/2.54+16 --> N=~72.
Answer: E.
Answer: (E) 72
Question: Find the average of first 100 natural numbers?
(A) 50.5
(B) 52
(C) 60.5
(D) 75
(E) 65
Rationale: Sum of first 100 natural numbers = 100*101/2 = 5050
Required average = 5050/100 = 50.5
Answer is A
Answer: (A) 50.5
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value T?
(A) 2r
(B) 2s
(C) r +s
(D) 2r-s
(E) 2s-r
Rationale: The simplest way to do this is to assume values.
We are told that r and s are positive integers T.
Also, r-s = 6 => r = 6+s
Hence r is 6 more than s.
Let s be 10. Hence r = 16.
Option A: 2r = 2*16 = 32
Option B: 2s = 2 * 10 = 20
Option C: r + s = 16 + 10 = 26
Option D: 2r - s = 2(16) - 10 = 32 - 10 = 22
Option E: 2s - r = 2(10) - 16 = 20 - 16 = 4
Hence option A is the greatest.
Answer: (A) 2r
Question: Of the 16 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 16 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
(A) 22
(B) 35
(C) 56
(D) 110
(E) 105
Rationale: another approach :
one scenario : [WWWM]
now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.
and 11 ways to select one man
so 5*4*3*11 = 660
now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways
hence 660/3!= 660/6=110
D
Answer: (D) 110
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
(A) 288
(B) 277
(C) 209
(D) 992
(E) 612
Rationale: (800*3*3)/100 = 72
920 + 72 = 992
Answer: D
Answer: (D) 992
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit C on this shipment?
(A) a) $100
(B) b) $115
(C) c) $125
(D) d) $130
(E) e) $135
Rationale: I recommend one should use fractions to solve this one rather than converting it into decimals
Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225
Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600
Profit C= 725-600 = $125
Ans:C
Answer: (C) c) $125
Question: At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Raja,Kamal, Baskar, and Divya get lockers with the numbers 350, 400, 150, and 420, respectively, who is the most popular student?
(A) Divya
(B) Kamal
(C) Baskar
(D) Raja
(E) They have equal popularity
Rationale: Distinct prime factors of 350 (Raja) : 2,5,7
Distinct prime factors of 400 (Kamal): 2 and 5.
Distinct prime factors of 150 (Baskar): 2,3, and 5
Distinct prime factors of 420 (Divya): 2,3,5 and 7.
So most popular student - Divya
Answer A
Answer: (A) Divya
Question: The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell shorof the required amount. What is the amount by which he might have fallen short?
(A) 40
(B) 45
(C) 54
(D) 65
(E) 70
Rationale: Let the price of gift pack be 'aa'
Then number of packs bought =a+1=a+1
Hence total cost is a(a+1)a(a+1)
It is given that 380<a(a+1)380<a(a+1)
If a=19a=19, the total cost =19×20=380=19×20=380
Dexter would not have fallen short, If:
a=20a=20, a(a+1)=420a(a+1)=420
So he would have fallen short by Rs 40.
This is the minimum amount by which he may have fallen short.
A
Answer: (A) 40
Question: A train sets off at 2 p.m. at the speed of 70 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) 10.60 p.m
(B) 10.20 p.m
(C) 10.30 p.m
(D) 10.10 p.m
(E) 10.50 p.m
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer: C
Answer: (C) 10.30 p.m
Question: A bus leaves Santa Barbara at 6:00 a.m. traveling east at 50 miles per hour. At 2:00 p.m. a plane leaves Santa Barbara traveling east at 450 miles per hour. At what time will the plane overtake the bus?
(A) 2:45 p.m.
(B) 3:15 p.m.
(C) 3:30 p.m.
(D) 3:45 p.m.
(E) 3:00 p.m.
Rationale: At 2:00pm, the bus is 400 miles ahead of plane
The plane travels at 450 mph, which gains 400 mph on bus
400/400= 1 hour
2:00 + 1:00 = 3:00
The plane will overtake bus at 3:00pm
Answer:E
Answer: (E) 3:00 p.m.
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit?
(A) 3089
(B) 3098
(C) 3057
(D) 3000
(E) 3012
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
Answer: D
Answer: (D) 3000
Question: If two numbers are in the ratio 2:3. If 20 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) A)10
(B) B)20
(C) C)25
(D) D)30
(E) E)40
Rationale: 2:3
2x + 20 : 3x + 20 = 3 : 4
4[2x + 20] = 3[3x + 20]
8x + 80 = 9x + 60
9x - 8x = 80 - 60
x = 20
Then smallest number is = 2
2x = 40
Correct Option E
Answer: (E) E)40
Question: Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team Q, but each box of Team A’s has 60% fewer booklets than each box of Team Q’s. Which of the following could be the total number of booklets distributed by the two groups?
(A) 2,000
(B) 3,200
(C) 4,100
(D) 4,800
(E) 4,900
Rationale: Let x be the no of booklets in each box that team Q distributes. So, Team A has 60% fewer - 0.4x.
Let y be the no. of boxes distributed by team Q. So, Team A distributes 60% more - 1.6y
Total booklets distributed by team A = xy
Total booklets distributed by team Q=0.64xy
Total booklets distributed = xy+0.64xy=1.64xy
As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.
Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.
Similarly all answer choices, except choice C, fail to provide an integer value.
Choice C = 4100/1.64= 2500 and is the correct answer.
Answer: (C) 4,100
Question: A is twice as good a work man as B and together they finish the work in 4 days. In how many days A alone can finish the work?
(A) 3
(B) 2
(C) 7
(D) 9
(E) 6
Rationale: WC = 2:1
2x + x = 1/4 => x = 1/12
2x = 1/6
A can do the work in 6 days.
Answer: E
Answer: (E) 6
Question: Set A consists of the integers from 1 to 12, inclusive, while set B consists of the integers from 5 to 15, inclusive. How many distinct integers do belong to the both sets at the same time?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 9
Rationale: A = {1,2,3,4, 5,6, 7, 8, 9, 10, 11, 12}
B = {5,6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
Common elements = {5,6, 7, 8, 9, 10, 11, 12} = 8 elements
Answer: Option A.
Answer: (A) 8
Question: Kyle is a lumberjack with 12 trees to cut down. How many ways can he cut down one or more of the trees today?
(A) 255
(B) 4095
(C) 1023
(D) 8125
(E) 513
Rationale: Kyle can cut down one or more of 12 trees
=> 2 ^ 12 - 1 = 4095
B
Answer: (B) 4095
Question: There are 9 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played?
(A) 24
(B) 25
(C) 28
(D) 32
(E) 36
Rationale: 9C2 = 36
The answer is E
Answer: (E) 36
Question: The quantity of water needed to reduce 9 ml shaving lotion containing 50% alcohol to a lotion containing 30% alcohol is?
(A) 6ml
(B) 10ml
(C) 5.5ml
(D) 8ml
(E) 9.3ml
Rationale: Quantity of alcohol in 9ml lotion = 50/100 *9 = 4.5ml
Let the water added be x ml
4.5 / 9+x = 30/100
x = 6ml
Answer is A
Answer: (A) 6ml
Question: What was the principal , if at 5% per annum the interest after 10 years amounted to Rs.3100 less than the sum lent?
(A) 6200
(B) 3000
(C) 3000
(D) 2000
(E) 1000
Rationale: P - 2336 = (P*10*5)/100
P = 6200
Answer: A
Answer: (A) 6200