mathewhe/aqua_rat huggingface dataset:
Question: A cylindrical can has a radius of 6 centimeters and a height of 12 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
(A) 16 pi
(B) 64 pi
(C) 96 pi
(D) 144 pi
(E) 576 pi
Rationale: They are asking the lateral surface area of the cylinder.
the Lateral surface area = 2* pi * r *h
= 2*pi*6*12=144 pi
Answer is D.
Answer: (D) 144 pi
Question: Find the product of the localvalue and absolutevalue of 4 in 20468?
(A) 1000
(B) 1100
(C) 1200
(D) 1300
(E) 1600
Rationale: Local value of 4 = 4 x 100 = 400
Place value of 4 = 4
There fore = 4 x 400 = 1600
E
Answer: (E) 1600
Question: Set A contains three different positive odd integers and three different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?
(A) 3/5
(B) 2/5
(C) 1/2
(D) 4/5
(E) 19/25
Rationale: There can be an odd product only if both integers are odd.
P(odd product) = 1/2*2/5 = 1/5
P(even product) = 1 - 1/5 = 4/5
The answer is D.
Answer: (D) 4/5
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 9 p.m. from Delhi. When will they meet?
(A) 40.00 a.m.
(B) 10.00 a.m.
(C) 12.00 a.m.
(D) 11.00 a.m.
(E) 19.00 a.m.
Rationale: Explanation:
D = 110 â€“ 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
9 a.m. + 2 = 11 a.m.
Answer: Option D
Answer: (D) 11.00 a.m.
Question: If p/q =4/5, then the value of 25/7 + {(2q - p) / (2q + p)} is ?
(A) 4
(B) 34
(C) 1
(D) 2
(E) 3
Rationale: Answer
Given Exp. = 25/ 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 25/7 + {2-p/q) / (2 + p/q)}
= 25/7 + {(2 - 4/5) / (2 + 4/5)}
= 25/7 + 6/14
= 25/7 + 3/7
=28/7
=4
Correct Option: A
Answer: (A) 4
Question: In what time will two trains cross each other completely, which are running on the same parallel lines in opposite directions, each 100 m in length both trains running with a speed of 80 kmph?
(A) 4.5 sec
(B) 4.8 sec
(C) 4.2 sec
(D) 5.0 sec
(E) 5.2 sec
Rationale: D = 100m + 100m = 200m * 1/1000 = 0.2 kms
RS = 80 + 80 = 160 kmph
T = (0.2/160) * 3600 = 4.5 sec
ANSWER:A
Answer: (A) 4.5 sec
Question: 14, 35, 49, 56, 91, 126
In the sequence above, each term is related with the others. Which of the following could not be a term in the sequence?
(A) 560
(B) 259
(C) 562
(D) 686
(E) 847
Rationale: Simplifying the question into easier words we just need to find which of the numbers is not divisible by 7
clearly the answer is 562 because if we divide 562 by 7 we get a remainder of 80.28
Correct answer - C
Answer: (C) 562
Question: The product of all the prime numbers less than 12 is closest to which of the following powers of 10?
(A) a) 10^9
(B) b) 10^8
(C) c) 10^7
(D) d) 10^3*2.31
(E) e) 10^5
Rationale: Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11)= 10*21*11
Now take out power of 10 from each number and rewrite
10*10*10(1*2.1*1.1) or 10^3*(1*2.1*1.1) =2.31*10^3
D
Answer: (D) d) 10^3*2.31
Question: An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
(A) 1/5
(B) 3/7
(C) 2/5
(D) 3/5
(E) 2/7
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 10/15
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 9 black balls and five white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 9/14
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 10/15 × 9/14 = 3/7
B
Answer: (B) 3/7
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
(A) Rs.15009
(B) Rs.15029
(C) Rs.15072
(D) Rs.15000
(E) Rs.15021
Rationale: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit
= 3/5 * 25000
= Rs.15000
Answer: D:
Answer: (D) Rs.15000
Question: Three positive integers a, b, and c are such that their average is 18 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
(A) 21
(B) 23
(C) 25
(D) 27
(E) 29
Rationale: Solution:
We know that the average value is 18 therefore (a+b+c)/3 = 18
so a+b+c = 54
and b = a + 11
therefore a + (a + 11) + c = 54
The least value of c is when c = b
so take c = a + 11
hence, a + (a + 11) + (a + 11) = 54
i.e., a = 32/3 a non integer therefore c is not equal to b
so take c = b+1 therefore c = a+12
a + (a + 11) + (a + 12) = 54
i.e., a= 31/3 again a non integer therefore c is not equal to b+1
next take c= b+2 therefore c = a+13
a + (a + 11) + (a + 13) = 54
i.e., a=30/3 = 10
hence, a = 10, b = 21, and c = 23
Answer: B
Answer: (B) 23
Question: At a summer camp with 1,200 participants, 1/2 of the campers are aged 8 to 12. Next year, the number of campers aged 8 to 12 will increase by 1/3. After this change, what percentage of the total 1,200 campers will the 8- to 12-year-olds represent?
(A) 66 2/3%
(B) 60%
(C) 50%
(D) 45%
(E) 40%
Rationale: Total - 1,200 participants
campers are aged 8 to 12 = (1/2)*1200 = 600
Next year, campers are aged 8 to 12 = (4/3)*600 = 800
Percentage = (800/1200)*100 = 66 2/3%
Answer: Option A
Answer: (A) 66 2/3%
Question: Niall's income is 60% less than Rex's income, and Sam's income is 25% less than Niall's income. If Rex gave 60% of his income to Sam and 40% of his income to Niall, Niall's new income would be what fraction of Sam's new income?
(A) 8/9
(B) 11/12
(C) 8/13
(D) 11/13
(E) 12/13
Rationale: We can take some easy numbers and make calculations simpler.
Let R ( Rex's income) = 100
Q (Niall's income) = 40%R = 40
S (Sam's income) = 75% Q = (3/4)*40 = 30
Now, if Rex gives 40% to Niall --> Q = 40 + 40 = 80
60% given to Sam --> S = 30+60 = 90
The ratio is : Q/S = 80/90 = 8/9= A
Answer: (A) 8/9
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 160 m long?
(A) 41.6 sec
(B) 11 sec
(C) 88 sec
(D) 19 sec
(E) 10 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 160 = 520 m
Required time = 520 * 2/25 = 41.6 sec
Answer: A
Answer: (A) 41.6 sec
Question: How many kgs of flour worth 25 per kg must be blended with 30 kgs of flour worth ` 30 per kg so that by selling the blended variety at X 30 per kg there should be a gain of 10%?
(A) 32 kg
(B) 40 kg
(C) 36 kg
(D) 42 kg
(E) None of these
Rationale: (x * 25) + (30 * 30) / (x + 30)
= 11/10 * 30(x + 30)
On solving the equation, x = 36.
Answer:C
Answer: (C) 36 kg
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 288
(B) 280
(C) 268
(D) 256
(E) 876
Rationale: x*(85/100)
= (480 - x)119/100
x = 280
Answer:B
Answer: (B) 280
Question: The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. How many workers are there in the workshop?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: Explanation:
Let the number of workers = x
Given that average salary of all the workers = Rs.8000
Then, total salary of all workers = 8000x
Given that average salary of 7 technicians is Rs.12000
=> Total salary of 7 technicians = 7 × 12000 = 84000
Count of the rest of the employees = (x - 7)
Average salary of the rest of the employees = Rs.6000
Total salary of the rest of the employees = (x - 7)(6000)
8000x = 84000 + (x - 7)(6000)
=> 8x = 84 + (x - 7)(6)
=> 8x = 84 + 6x - 42
=> 2x = 42
=> x = 42/2 = 21
Answer: Option A
Answer: (A) 21
Question: I had about Rs.14.40 in one rupee coins and 20 paise coins when I went out for shopping.
When I returned, I found that number of 20 paise coins and 1 rupee coins are exactly as 1
rupee and 20 paise coins respectively, that I had originally. I came back with one third of
what I had started out with. How many one rupee coins did I have initially?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Let x be number of 1 rupee coins and y be number of 20 paise coins initially.
Initially : 1x + .2y =14.40
Finally : 1y + .2x = 4.80 (as number of coins interchange)
Solving we get, x=14 and y=2
Therefore there was 14 one rupee coins and 2 20 paise coins initially.
ANSWER:C
Answer: (C) 14
Question: If f and p are two positive integers and f/p = 1.35, then f can equal which one of the following?
(A)  21
(B)  28
(C)  20
(D)  27
(E)  23
Rationale: f/p = 1.35 = 135/100 = 27/20
So, p COULD equal 27
Answer: D
Answer: (D)  27
Question: During the first two weeks of March, the total rainfall in Springdale was 25 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall in inches during the second week of March?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 18
Rationale: Let x be the rainfall in the first week. Then 1.5x was the rainfall in the second week.
2.5x = 25
x = 10
The rainfall during the second week was 1.5 * 10 = 15 inches
The answer is C.
Answer: (C) 15
Question: subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 30 pages.
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 30 page's copy =(30/2.5)=12 hrs
ANSWER:C
Answer: (C) 12
Question: One fourth of a solution that was 12% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight?
(A) 28%
(B) 34%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: consider total solution to be 100 liters and in this case you'll have: 75*0.12+25*x=100*0.16 --> x=0.28.
Answer: A.
Answer: (A) 28%
Question: Daniel went to a shop and bought things worth Rs. 25, out of which 60 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) A)14.4
(B) B)20
(C) C)21.3
(D) D)21.5
(E) E)22
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 60 Paise = Rs.60/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−60/100−x)6/100 = 60/100
⇒ 6(25 −0.6 −x) = 60
⇒ (25 − 0.6 − x) = 10
⇒ x = 25 − 0.6 − 10 = 14.4
A
Answer: (A) A)14.4
Question: how many such letters pairs are in word MONKEY having same no. of letters left between them in the word as they have in the series
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: one pair is observed that is (ON) as there is no alphabet in between them and in series also threre is no letter in between them.
ANSWER:A
Answer: (A) 1
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 42 seconds
(B) 47 seconds
(C) 40 seconds
(D) 49 seconds
(E) 45 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C
Answer: (C) 40 seconds
Question: How many multiples of 8 are less than 4500, and also multiples of 12?
(A) 104.6
(B) 187.5
(C) 625.6
(D) 450.5
(E) 467.4
Rationale: LCM of 8 & 12 = 24
Tried dividing 4500 by 24
Got quotient 187.5 'So B is answer
Answer: (B) 187.5
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 20% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 10%. If Ron imported a $20,000 imported car and ended up paying $2500 in taxes, what is the first tier's price level?
(A) $6000
(B) $5500
(C) $5000
(D) $5700
(E) $5800
Rationale: Let T be the tier price, P be total price = 20000
Per the given conditions:
0.20T + 0.10(P-T) = 2500
0.20T+0.10*20000-0.10T =2500
0.10T +2000 =2500
0.10T = 2500-2000 = 500
T = 500/0.10 =5000
Answer C
Answer: (C) $5000
Question: In six successive games, a baseball team scored 4 runs once, 7 runs twice, and 10 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: 4 runs once (one game)
7 runs twice (two game)
10 runs three times (three games)
SO we have (4*1 + 7*2 + 10*3)/6 = 48/6 = 8.
ANS: A.
Answer: (A) 8
Question: A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?
(A) 2
(B) 3
(C) 6
(D) 12
(E) 14
Rationale: Explanation:
Since B and D are twins, so B = D.
Now, A = B + 3 and A = C - 3.
Thus, B + 3 = C - 3 D + 3 = C-3 C - D = 6.
Answer: C
Answer: (C) 6
Question: If 20% of a number = 200, then 120% of that number will be?
(A) 20
(B) 120
(C) 360
(D) 1200
(E) 820
Rationale: Let the number x. Then,
20% of x = 200
x = (200 * 100)/20 = 1000
120% of x = (120/100 *1000) = 1200.
ANSWER:D
Answer: (D) 1200
Question: When positive integer x is divided by positive integer y, the remainder is 8. If x/y = 96.16, what is the value of y?
(A) 96
(B) 75
(C) 50
(D) 25
(E) 12
Rationale: by the definition of a remainder, the remainder here is equal to 8/y. the remainder in decimal form is given as .16
therefore, 8/y = .16
solve for y and get 50.
C
Answer: (C) 50
Question: The circumferences of two circles are 660 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 2996 sq m
(B) 4774 sq m
(C) 4312 sq m
(D) 2768 sq m
(E) 2786 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 660 and 2∏l = 704
s = 660/2∏ and l = 704/2∏
Difference between the areas = ∏l^2 - ∏s^2
= ∏{330^2/∏^2 - 352^2/∏^2}
= 330^2/∏ - 352^2/∏
= (330 - 352)(330 + 352)/∏
= (22)(682)/(22/7)
=4774 sq m
Answer:B
Answer: (B) 4774 sq m
Question: How many positive integers will divide evenly into 530?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
Rationale: 520 = 10*13*4 = 8*5*13 = 2^3*5*13
We need to positive integers will divide evenly into 520 or simply the factors of 520
If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)
Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 18
Option D
Answer: (D) 18
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 881
(C) 711
(D) 622
(E) 211
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
Answer: (A) 230
Question: Ratio of two numbers x and y is 7:9. If x is increased by 20% and y is increased by 33 then the new ratio becomes 1:5. What is the ratio 2y:(x+4)
(A) 18:11
(B) 8:1
(C) 11:18
(D) 1:8
(E) 1:1
Rationale: Let:
x = 7n
y = 9n
8.4n/(9n+33) = 1/5
42n = 9n+33
n = 1
So, x =7; y=9
2y/(x+4) = 18/11
Answer = A
Answer: (A) 18:11
Question: In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 45% of all the employees are men .What % of all the employee went to the picnic?
(A) 31%
(B) 34%
(C) 35%
(D) 36%
(E) 37%
Rationale: total men in company 45% means total women in company 55%(assume total people in company 100%)
no of men employees attended picnic=45x(20/100)=9
no of women employees attend picnic=55x(40/100)=22
total percentage of employees attend the picnic=9+22=31%
ANSWER:A
Answer: (A) 31%
Question: 200,190,180,....,160,150,140
Insert the missing number
(A) 155
(B) 156
(C) 157
(D) 170
(E) 158
Rationale: Missing number : 170
Answer : D
Answer: (D) 170
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
(A) 120
(B) 720
(C) 4320
(D) 2160
(E) 3570
Rationale: The word 'OPTICAL' contains 7 different letters.
when the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA)
Now, 5 letters can be arranged among themselves in 3!=6 ways.
Required number of ways =(120*6)=720.
Answer is B
Answer: (B) 720
Question: Two members of a certain club are selected to speak at the next club meeting. If there are 45 different possible selections of the 2 club members, how many members does the club have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 10
Rationale: Method-1
Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]
i.e. If total member = n
then nC2 = n! / [(2!)(n-2)!] = 45
i.e. n*(n-1)*n-2!/ [(2!)n-2!] = 45
i.e. n*(n-1) = 90
(for Positive Values of n)
therefore, n*(n-1) = 90
i.e. n= 10
Answer: Option E
Answer: (E) 10
Question: From among the 35 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
(A) 1360
(B) 1260
(C) 1060
(D) 1190
(E) 1460
Rationale: There are 35 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 35 ways. When one person is appointed as leader, we are left with 35 students. Out of these 34 teachers, we can select one class representative. So, a class representative can be selected in 34 ways. Hence, the number of ways in which a leader and class representative can be selected = 35 x 34 = 1190
ANSWER:D
Answer: (D) 1190
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 70 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
(A) 22
(B) 10
(C) 25
(D) 99
(E) 21
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 70) = 90(x - 5)
100 = 10x => x = 10.Answer: B
Answer: (B) 10
Question: Seats for Maths, Physics and Biology are in the ratio of 4 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
(A) 2 : 3 : 4
(B) 6 : 7 : 8
(C) 8 : 15 : 20
(D) Cannot be determined
(E) None of these
Rationale: Reqd ratio 4 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100
= 4 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 8 : 15 : 20
Answer C
Answer: (C) 8 : 15 : 20
Question: A 5" cube is painted in all its faces and then it is cut down into 1" blocks. How many 1" blocks
are there even without a single face being painted?
(A) 16 blocks
(B) 20 blocks
(C) 27 blocks
(D) 36 blocks
(E) 64 blocks
Rationale: The unpainted blocks are the interior blocks.
These blocks form a 3" cube on the inside.
The number of unpainted blocks is 3*3*3 = 27 blocks.
The answer is C.
Answer: (C) 27 blocks
Question: At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $5 on candy, how much did John spend at the supermarket?
(A)  $75
(B)  $80
(C)  $90
(D)  $120
(E)  $180
Rationale: Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.
We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $5 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:
(1/2)T + (1/3)T + (1/10)T + 5 = T
To get rid of the fractions we can multiply the entire equation by 30, and we obtain:
15T + 10T + 3T + 150 = 30T
28T + 150 = 30T
150 = 2T
T = 75
John spent $7 at the supermarket.
Answer: A
Answer: (A)  $75
Question: In how many ways can the letters of the word TATTOO be arranged?
(A) 1206
(B) 1348
(C) 2520
(D) 60
(E) 3478
Rationale: TATTOO has 6 words, but T is repeated three times and O is repeated two times. Thus ways
= 6! / 3!2! = 60 ways
D
Answer: (D) 60
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 45 years. What will be the age of the B ten years hence?
(A) 22
(B) 77
(C) 26
(D) 96
(E) 90
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 45 => b + c = 90 --- (2)
From (1) and (2), we cannot find b.
Answer: E
Answer: (E) 90
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1134
(B) 1234
(C) 1257
(D) 1259
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: A club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 10 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 12
Rationale: As no member of committee M is on either of the other 2 committees then 30-M=30-8=22 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees
General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 22-10=12 is the greatest possible number of members in the club who are on none of the committees.
Answer: E.
Answer: (E) 12
Question: If x^2+4x+3 is odd, then which one of the following could be the value of x.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 9
Rationale: for any x, 4x+3->odd
so x^2 should be even, means x should be even;
only ans we have 4 as even.
ANSWER:B
Answer: (B) 4
Question: Which is the following is divisible by 11
(A) A)109
(B) B)4825
(C) C)4805
(D) D)4905
(E) E)4906
Rationale: Explanation:
Sum of first 'n' natural numbers = 1(1 + 1)/2
Sum of first 9 natural numbers = 1(1 + 1)//2 = 1 x 1= 1
Sum of first 99 natural numbers = 11(11 + 1)//2 = 11 x 10 = 110
110 - 1 = 109
Answer: Option A
Answer: (A) A)109
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 76 sec
(B) 16 sec
(C) 15 sec
(D) 17 sec
(E) 19 sec
Rationale: Speed = 63 * 5/18
= 35/2 m/sec
Time taken
= 280 * 2/35
= 16 sec
Answer: B
Answer: (B) 16 sec
Question: A cycle is bought for Rs.840 and sold for Rs.1220, find the gain percent?
(A) 70%
(B) 45%
(C) 48%
(D) 30%
(E) 40%
Rationale: Explanation:
840 ---- 380
100 ---- ? => 45%
Answer: B
Answer: (B) 45%
Question: The average of 35 students in a class is 17 years. The average age of 25 students is 15. What is the average age of remaining 10 students?
(A) 26 years
(B) 27 years
(C) 28 years
(D) 29 years
(E) 30 years
Rationale: Sum of the ages of 14 students
= (17 * 35) - (15 * 21) = 595 - 315 = 280
Required average = (280/10) = 28 years.
Answer:C
Answer: (C) 28 years
Question: In what ratio should rice at Rs.9.30 per Kg be mixed with rice at Rs. 10.80 per Kg so that the mixture
be worth Rs.10 per Kg ?
(A) 7 : 8
(B) 8 : 7
(C) 6 : 7
(D) 7 : 6
(E) None of these
Rationale: Explanation :
By the rule of alligation, we have
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
9.3 10.80
Mean Price
10
10.8-10 = .8 10 - 9.3 = .7
Required ratio = .8 : .7 = 8 : 7.
Answer : Option B
Answer: (B) 8 : 7