mathewhe/aqua_rat huggingface dataset:
Question: 6 2/3 * 9 3/5 * 2 1/3 + 1 1/3 = ?
(A) 150 1/3
(B) 150 2/3
(C) 149 2/3
(D) 149 1/3
(E) None of these
Rationale: Explanation:
6 2/3 * 9 3/5 * 2 1/3 + 1 1/3 = 20/3 * 48/5 * 7/3 + 4/3
= 448/3 + 4/3 = 452/3 = 150 2/3
ANSWER IS B
Answer: (B) 150 2/3
Question: Parameshwaran invested an amount of 12,000 at the simple interest rate of 10 pcpa and another amount at the simple interest rate of 20 pcpa. The total interest earned at the end of one year on the total amount invested became 14 pcpa. Find the total amount invested
(A) 22,000
(B) 25,000
(C) 20,000
(D) 24,000
(E) None of these
Rationale: Let the amount invested at 20% rate be x. According to the question,
12000 × 10⁄100 + x × 20⁄100 = (12000 + x) × 14⁄100
or, 1200 + x⁄5 = 1680 + 7⁄50x
or, x⁄5 - 7⁄50x = 480
or, 3⁄50x = 480
\ x = 8000
\ Total amount invested = (12000 + 8000)= 20000
Answer C
Answer: (C) 20,000
Question: P can do a work in 60 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
(A) 7
(B) 8
(C) 9
(D) 15
(E) 25
Rationale: Work done by P in 1 day = 1/60
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3Ã—7/36 = 7/12
Remaining work = 1 â€“ 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/60) = 25
Option E
Answer: (E) 25
Question: If the price of 25 toys is 500, then what will the price of 10toys ?
(A) 144
(B) 361
(C) 117
(D) 287
(E) 200
Rationale: One toy price = 500/25 = 20
10 toy price = 10 * 20 = 200
Answer : E
Answer: (E) 200
Question: There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?
(A) 43
(B) 54
(C) 65
(D) 91
(E) 99
Rationale: We first count the number of committee in which
(i). Mr. Y is a member
(ii). the ones in which he is not
case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).
We can choose 1 more in5+\inline {\color{Blue} 2C_{1}}=7 ways.
case (ii): If Mr. Y is not a member then we left with (6+4-1) people.
we can select 3 from 9 in \inline {\color{Blue} 9C_{3}}=84 ways.
Thus, total number of ways is 7+84= 91 ways.
D
Answer: (D) 91
Question: The average of five integers is 71, and none of these integers is greater than 100. If the average of three of the integers is 76, what is the least possible value of one of the other two integers?
(A) 5
(B) 15
(C) 20
(D) 21
(E) 27
Rationale: When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 71
So, the sum of ALL 5 integers = (71)(5) =355
The average of three of the integers is 65
So, the sum of the 3 integers = (76)(3) =228
So, the sum of the 2 REMAINING integers =355-228=127
If the sum of the 2 REMAINING integers =127, and we want to minimize one value, we must MAXIMIZE the other value.
100 is the maximum value so let 1 integer = 100, which means the other must equal 27
Answer: E
Answer: (E) 27
Question: There are 8 books on a shelf that consist of 3 paperback books and 5 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
(A) 35
(B) 45
(C) 50
(D) 55
(E) 65
Rationale: The total number of ways to select 4 books is 8C4 = 70
The number of ways which do not include any paperbacks is 5C4 = 5
The number of combinations with at least one paperback is 70-5 = 65
The answer is E.
Answer: (E) 65
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
(A) 1 hr
(B) 3 hr
(C) 2 hr
(D) 6 hr
(E) 8 hr
Rationale: A
1 hr
Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr
Answer: (A) 1 hr
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 40 per cent. The two reductions together are equal to a single reduction of
(A) 45%
(B) 55%
(C) 35%
(D) 32.5%
(E) 30%
Rationale: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 40percent is reduced which means the new price is merely 60percent of 3/4P
==> (3/4)x(3/5)P = 9/20P is the new price after both deduction which is 45percent of the original value P. This implies this entire series of deduction is worth having discounted 55% of P. So answer is B = 55%
Answer: (B) 55%
Question: One pump drains one-half of a pond in 8 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
(A) 1 hour
(B) 1.1 hour
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: First pump drains 1/2 of the tank in 8 hours
so 16 hours it will take to drain the full tank.
Let, 2nd pump drains the full tank in a hours
so both together can drain (1/16+1/a) part in 1 hour
son in 1/2 hour they drain 1/2*(1/16+1/a) part of the tank
given that in 1/2 hour they drain 1/2 of the tank
hence we can say
1/2*(1/16+1/a) = 1/2
solving u get a = 16/15=1.1
Hence answer is B
Answer: (B) 1.1 hour
Question: At what rate of compound interest per annum will a sum of $1200 becomes 1348.32 in 2 years?
(A) 5%
(B) 6%
(C) 7%
(D) 8%
(E) 10%
Rationale: Let the rate be R% p.a.
1200*(1+R/100)^2 = 1348.32
(1+R/100)^2 = 134832/120000 = 11236/10000
(1+R/100)^2 = (106/100)^2
1+R/100 = 106/100
R = 6%
Answer is B
Answer: (B) 6%
Question: The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $48.0 billion from $72.0 billion, a year ago. By what percent did the revenue fall?
(A) 20.8
(B) 30.4
(C) 31.8
(D) 32.5
(E) 33.3
Rationale: $72-$48=24$
(24/72)*100=33.33%
ANSWER:E
Answer: (E) 33.3
Question: If two numbers are in the ratio 5:2. If 20 is subtracted from both of the numbers then the ratio becomes 4:2 then find the smallest number?
(A) 30
(B) 20
(C) 40
(D) 50
(E) 12
Rationale: 5:2
5x - 20 : 3x - 20 = 4 : 2
2[5x - 20] = 4[3x - 20]
10x - 40 = 12x - 80
12x - 10x = 80 - 40
x = 20
Then smallest number is = 2x
2x = 40
C
Answer: (C) 40
Question: A train 150 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
(A) 54 kmph
(B) 60 kmph
(C) 66 kmph
(D) 72 kmph
(E) 84 kmph
Rationale: speed of train relative to man: 150/6 * 18/5 km/hr
= 90 km/hr
let speed of train= x
therefore x+6 = 90
x= 90-6
x=84 km/hr
ANSWER:E
Answer: (E) 84 kmph
Question: In his pocket, a boy has 3 red marbles, 5 blue marbles, and 5 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: The worst case scenario would be that he has taken 5 blue and 5 green, a total of 10 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 11, will surely be red as only the red marbles are left in his pocket.
The answer is C.
Answer: (C) 11
Question: Of 800 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?
(A) 20
(B) 25
(C) 30
(D) 55
(E) 100
Rationale: Say the number of students who read book A is A and the number of students who read book B is B.
Given that 20% of those who read book A also read book B and 25% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.25B --> A=1.25B.
Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 800=1.25B+B-0.25B --> B=400, A=1.25B=500 and {Both}=0.25B=100.
The number of students who read only book A is {A}-{Both}=500-100=400;
The number of students who read only book B is {B}-{Both}=400-100=300;
The difference is 400-300 = 100.
Answer: E.
Answer: (E) 100
Question: What is the ratio W of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 3/5
(E) 2
Rationale: Let X be the side of the cube. Therefore X^2*6= surface area.
the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.
6X^2/10X^2 = 3/5 = W.
Answer = D
Answer: (D) 3/5
Question: A fruit seller had some apples. He sells 40% apples and still he has 420. Originally he had how many apples?
(A) 400
(B) 500
(C) 700
(D) 450
(E) 650
Rationale: Suppose originally he had x apples
then (100-40)% of x = 420
60x/100 = 420
x= 700
Answer is C
Answer: (C) 700
Question: If two girls starting from same point, walking in the opposite directions with 5km/hr and 10km/hr as average speeds respectively. Then the distance between them after 5 hours is?
(A) 45
(B) 55
(C) 65
(D) 75
(E) 85
Rationale: Explanation:
Total distance = Distance traveled by person A+ Distance traveled by person B
= (5Ã— 5) + (10Ã— 5)
= 25+ 50
= 75 Km
Answer:D
Answer: (D) 75
Question: Exactly 10% of the reporters for a certain wire service cover local politics in Country X. If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
(A)  20%
(B)  42%
(C)  44%
(D)  85%
(E)  84%
Rationale: You are correct. People who cover local politics are a subset of people who cover politics.
30% of reporters who cover politics do not cover local politics so 70% DO cover local politics.
Reporters covering local politics= 70% of reporters covering politics= 10% of all reporters
Reporters covering politics/All Reporters = 10/70 = 1/7
Reporters not covering politics/All Reporters = 6/7 = 85%=D
Answer: (D)  85%
Question: Mary sold boxes of butter cookies. Ann sold 5 times as much as she did. 18 boxes of cookies were sold that day, how many boxes did Mary sell?
(A) 3
(B) 5
(C) 6
(D) 10
(E) 18
Rationale: # of boxes of cookies Mary sold = x
Ann sold 5 times more = 5x
x + 5x = 18
6x = 18
x = 18/6 = 3
ANSWER: A
Answer: (A) 3
Question: The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 2 and 4 slices per customer. How many slices cannot be bought?
(A) 42.
(B) 38.
(C) 33.
(D) 22.
(E) 20.
Rationale: Let X pizzas of 2 slices and Y pizzas of 4 slices.
2X + 4Y.
Lets check options wise.
A. 42 => 2(15) + 4(3)
B. 38 => 2(15) + 4(2)
C. 33 = we can't write anything with 5 and 8 series..Lets try 2(15) + 4(3) = 32 , 2(16) + 4(3) = 34 , nothing works out.
D. 22 => 2(10) + 4(3)
E. 20 => 2(6) + 4(2)
Answer: correct option is C
Answer: (C) 33.
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, ?, 2, 1
(A) 1
(B) 3
(C) 5
(D) 8
(E) 9
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
D
Answer: (D) 8
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 3 boys when a boy gets any no. of prizes?
(A) 55
(B) 58
(C) 64
(D) 65
(E) 27
Rationale: Ans.(E)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (3 x 3 x 3) ways = 33 ways = 27 ways Or nr ways = 33 ways = 27 ways
Answer: (E) 27
Question: In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly?
(A) 1/4
(B) 1/2
(C) 3/5
(D) 9/10
(E) 16/20
Rationale: P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/5*1/4 = 9/10.
Answer: D.
Answer: (D) 9/10
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 150 m long?
(A) 38 sec
(B) 35 sec
(C) 44 sec
(D) 40.8 sec
(E) none of these
Rationale: Speed = 45 km/hr = 45 Ã— (5/18) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 150 = 510 meter
Time taken to cross the platform = 510/(25/2) = 510 Ã— 2/25 = 40.8 seconds
ANSWER:D
Answer: (D) 40.8 sec
Question: If x + y = 3 and x – y = 3, then x^2 - y^2 =
(A) -4
(B) 4
(C) 10
(D) 9
(E) 40
Rationale: The fastest approach has already been shown. Here's one more option.
Given:
x + y = 3
x – y = 3
Add the two equations to get: 2x = 6, which means x = 3
If x = 3, we can plug that value into either equation, to conclude that y = 0
If x = 3 and y = 0, then x² - y² = 9
Answer: D
Answer: (D) 9
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 76 kg
(B) 76.5 kg
(C) 85 kg
(D) Data inadequate
(E) None of these
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer: Option C
Answer: (C) 85 kg
Question: A certain country had a total annual expenditure of $2.4 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure?
(A)  $ 500
(B)  $1,000
(C)  $2,000
(D)  $3,000
(E)  $5,000
Rationale: Total expenditure / Population = per capita expenditure
Hence, (2,4 x 10^11) / 240 000 000 = (2,4 x 10^11) / (2,4 x 10^8) = 1 x 10^(11-8) =
1 x 10^3 = 1000.
Answer is B.
Answer: (B)  $1,000
Question: A, B, C together started a business. A invested Rs.5000 for 5 months B invested Rs.3000 for 6 months and C Rs.7000 for 3 months. If they get a total profit of Rs.7600. Find the share of A?
(A) 2999
(B) 2500
(C) 2777
(D) 2999
(E) 17212
Rationale: 5*5:3*6:7*3
25 : 30 : 21
25/76 * 7600 = 2500
Answer:B
Answer: (B) 2500
Question: A cycle is bought for Rs.900 and sold for Rs.1260, find the gain percent?
(A) 40%
(B) 20%
(C) 80%
(D) 30%
(E) 24%
Rationale: 900 ---- 360
100 ---- ? => 40%
Answer: A
Answer: (A) 40%
Question: The sum of two numbers is 45. Sum of their quotient and reciprocal is 2.05, Find the product of the numbers.
(A) 339
(B) 500
(C) 288
(D) 277
(E) 112
Rationale: Sol: Let a, b be the numbers.
a + b = 45
ab+baab+ba = 2.05
⇒a2+b2ab⇒a2+b2ab = 2.05
⇒(a+b)2−2abab=2.05⇒(a+b)2−2abab=2.05
⇒(a+b)2⇒(a+b)2 = 2.05ab + 2ab = 4.05ab
⇒⇒ ab = 4524.054524.05 = 500
Answer:B
Answer: (B) 500
Question: For positive integers m and n, which of the following can be written as n^2?
(A) m+2
(B) m+3
(C) m+1
(D) m+4
(E) m-2
Rationale: Plug values: if m=8, then m+1=9
The question asks which of the following CAN be written as y^2. If m=8, then m+1 CAN be written as 3^2.
Answer: D
Answer: (D) m+4
Question: A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 6 days, A finished the remaining work. In how many days A alone can finish the job?
(A) 10
(B) 25
(C) 60
(D) 8
(E) 20
Rationale: A+B 10days work = 10*1/40 = 1/4
Remaining work = 1-1/4 = 3/4
3/4 work is done by A in 6 days
whole work will be done by A in 6 *4/3 = 8days
Answer is D
Answer: (D) 8
Question: Jenny received a 10% raise each month for three consecutive months. What was her salary after the three raises if her starting salary was $2,000 per month?
(A) $2,248
(B) $2,300
(C) $2,331
(D) $2,410
(E) $2,662
Rationale: 2000 * 1.1 * 1.1 * 1.1 = 2000 * 1.331 = 2662
Answer: E
Answer: (E) $2,662
Question: A football team lost 5 yards and then gained 7. What is the team's progress?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: For lost, use negative. For gain, use positive.
Progress = -5 + 7 = 2 yards
A
Answer: (A) 2
Question: A train , having a length of 275 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
(A) 10 sec
(B) 8 sec
(C) 15 sec
(D) 4 sec
(E) 2 sec
Rationale: Explanation:
Distance = 275 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 275/(110/6) = 15 s
Answer: Option C
Answer: (C) 15 sec
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?
(A) 2837
(B) 2839
(C) 2834
(D) 2822
(E) 2823
Rationale: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 8720
32.5k = 32.5k/100k * 8720 = 2834
The number of valid votes polled in favour of B is 2834.
Answer:C
Answer: (C) 2834
Question: Rahim bought 65 books for Rs.1150 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ?
(A) 38
(B) 18
(C) 99
(D) 277
(E) 22
Rationale: Average price per book = (1150 + 920) / (65 + 50) = 2070 / 115 = Rs.18.Answer:B
Answer: (B) 18
Question: Solve for x: 2x – y = (3/4)x + 6.
(A) (y + 6)/5
(B) 4(y + 6)/5
(C) (y + 6)
(D) 4(y - 6)/5
(E) 5/4(y-6)
Rationale: Solution:
2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5.
correct answer B
Answer: (B) 4(y + 6)/5
Question: The average of 9 numbers is 7 and the average of 7 other numbers is 6. What is the average of all 16 numbers?
(A) 6 9/16
(B) 8
(C) 7 7⁄8
(D) 7 1⁄2
(E) 7 1⁄4
Rationale: The average of 9 numbers is 7....
The sum of those numbers is (9)(7) = 63.
The average of 7 other numbers is 6....
The sum of those numbers is (7)(6) = 42
The sum of ALL 16 numbers is 63+42 = 105. The average of those numbers is 105/16 = 6 9/16.
Final Answer:
[Reveal]Spoiler:
A
Answer: (A) 6 9/16
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 800 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
(A) 2880.
(B) 4860.
(C) 5780
(D) 5760
(E) 6380.
Rationale: Normal Day = 800 kw/h
Stormy Day = 800*1.2=960 kw/h
3 windmills for 2 hours on stormy day
960*3*2=5760
Answer: D
Answer: (D) 5760
Question: 3x^2 - x - 4 =
(A) (3x-4)(x-2)
(B) (3x-4)(x+2)
(C) (3x-4)(x-3)
(D) (3x-2)(x+1)
(E) none of above
Rationale: 3x^2 + 2x - 8
= 3x^2 + 3x - 4x - 4
= 3x (x + 1) - 4 (x+1)
= (3x-4) (x+1)
Option D
Answer: (D) (3x-2)(x+1)
Question: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of five metre is left from all sides of the boundary of the garden. What is the length of the garden?
(A) 32
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length
Also, 5 meter is left from all sides of the boundary of the garden.
Hence, length of the garden = (11 Ã— 2) + 5 + 5 = 32 meter
Answer is A.
Answer: (A) 32
Question: What number is that, to which, if its half be added, and from the sum 20 be subtracted, the remainder will be a fourth of the number itself?
(A) 16/3
(B) 16/2
(C) 16/4
(D) 16/1
(E) None
Rationale: let x be put for the number required.
Then by the conditions proposed, x + x/2 - 20 = x/4
And reducing the equation x = 16.
Proof, 16 + 16/2 - 20 = 16/4.
Answer C
Answer: (C) 16/4
Question: The greatest common factor of two positive integers is B. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?
(A) BY⁄Z
(B) XZ + YZ
(C) X⁄Z + Y
(D) X + Y⁄Z
(E) X + Z⁄Y
Rationale: Say other integer is W
Formula
GCF(WZ)*LCM(WZ) = W*Z
B*Y = W*Z
So W= BY/Z
Answer A
Answer: (A) BY⁄Z
Question: A woman has four blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
(A) 8
(B) 22
(C) 16
(D) 17
(E) 18
Rationale: total ways = 4*3*2=24..
now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..
the ways in which the pink blose and green skirty are together=1*1*2=2..
total ways =24-2=22..
B
Answer: (B) 22
Question: How many of the positive factors of 33 are not factors of 45?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Factors of 33 - 1, 3, 11, 33,
factors of 45- 1, 3, 5, 9, 15, 45,
Comparing both, we have three factors of 33 which are not factors of 45- 11, 33,
The answer is C
Answer: (C) 2
Question: A box contains ten bulbs out of which 5 are defective. If five bulbs are chosen at random, find the probability that atleast one bulb is good?
(A) 251/252
(B) 242/243
(C) 258/259
(D) 265/266
(E) 247/248
Rationale: Required probability=1-5C5/10C5= 1 - 1/252= 251/252Answer:A
Answer: (A) 251/252
Question: In how many ways can 5 people, A, B, C, D, E, be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
(A) 384
(B) 396
(C) 576
(D) 24
(E) 696
Rationale: Number of total arrangements = 5!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
5! - (4!*2*2) = 120 - (24*2*2) = 24
Answer D
Answer: (D) 24
Question: A box contains 3 blue marbles, 4 red, 5 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/364
(B) 2/455
(C) 1/91
(D) 4/455
(E) None of these
Rationale: Given that there are three blue marbles, four red marbles, five green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = 3C₃/14C₃ = (1 * 3 * 2 * 1)/(14 * 13 * 12) = 1/364
ANSWER:A
Answer: (A) 1/364
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 15 sec
(B) 16 sec
(C) 18 sec
(D) 20 sec
(E) 25 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
ANSWER: B
Answer: (B) 16 sec
Question: The cost of carpeting a room 18m long with a carpet 75cm wide at 45 paise per meter is Rs.81. The breadth of the room is:
(A) 7m
(B) 7.5metre
(C) 5.5m
(D) 6.5m
(E) 8.5m
Rationale: Length of the carpet= Total cost/ rate/m= 8100/45=180m
Area of the carpet= 180*75/100= 135m2
Breadth of the room = (Area/ length)= 135/18= 7.5m
ANSWER:B
Answer: (B) 7.5metre
Question: The area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?
(A) 40 m3
(B) 50 m3
(C) 60 m3
(D) 90 m3
(E) 40 m3
Rationale: Explanation:
lb = 20 ; lh = 15 ; fh = 12
(lbh)2 = 20 * 15 * 12 => lbh = 60 m3
Answer: Option C
Answer: (C) 60 m3
Question: -20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 5 greater than the preceding term. Which of the following could not be a term in the sequence?
(A) 0
(B) 200
(C) 440
(D) 665
(E) 762
Rationale: Ans : E 762
Since 762 is not divisible by 5 , all the other options are divisible by 5
Answer: (E) 762