mathewhe/aqua_rat huggingface dataset:
Question: The average marks of a class of 25 students is 50 and that of another class of 40 students is 65. Find the average marks of all the students?
(A) 52.6
(B) 52.4
(C) 52.1
(D) 59
(E) 52.9
Rationale: Sum of the marks for the class of 25 students = 25 * 50 = 1250
Sum of the marks for the class of 40 students = 40 * 65 = 2600
Sum of the marks for the class of 65 students =
1250 + 2600 = 3850
Average marks of all the students = 4850/65 = 59.Answer: D
Answer: (D) 59
Question: The speed of a train is 60 kmph. What is the distance covered by it in 20 minutes?
(A) 21 kmph
(B) 22 kmph
(C) 20 kmph
(D) 23 kmph
(E) 24 kmph
Rationale: 60 * 20/60
=20 kmph
Answer: C
Answer: (C) 20 kmph
Question: A car covers a distance of 624 km in 4 hours. Find its speed?
(A) 156
(B) 288
(C) 271
(D) 276
(E) 128
Rationale: 624/4 = 156 kmph
Answer: A
Answer: (A) 156
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
(A) 70
(B) 65
(C) 25
(D) 30
(E) 40
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
ANSWER A
Answer: (A) 70
Question: Reduce
368/598
to the lowest terms
(A) 30/25
(B) 28/13
(C) 28/29
(D) 8/13
(E) None of these
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 598 which is 46
Step2: Divide both by 46, we will get the answer 8/13
Answer: Option D
Answer: (D) 8/13
Question: A Complany provides health insurance that pays 50.0% of the cost, with a $180.00 deductible. This means that the employees pays the first $180.00, after which the insurance company pays 150.0%. How much will an employee pay if his total medical bill is $1400.00?
(A) $790
(B) $780
(C) $770
(D) $760
(E) $750
Rationale: Amount employee pays = 180 + 50/100* (1400-180)
= 180 + 50/100*1220
= 180+610
= $790
ANSWER:A
Answer: (A) $790
Question: In a school of 700 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
(A) 173
(B) 126
(C) 153
(D) 143
(E) 133
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
700 * 18/100 = 126
ANSWER:B
Answer: (B) 126
Question: The sum of the mean, the median, and the range of the set {1,5,6} equals which one of the following values?
(A) 7
(B) 12
(C) 14
(D) 17
(E) 20
Rationale: Here Mean => 1+5+6/3 => 4
median => 5
and range => 6-1 => 5
hence sum => 4+5+5=> 14
Answer: C
Answer: (C) 14
Question: If we have 9 people in a meeting, in how many ways they can sit around a table?
(A) 10*9!
(B) 9*8!
(C) 8*7!
(D) 7*6!
(E) 6*5!
Rationale: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=9
(n-1)!=8!=8*7!
Ans:C
Answer: (C) 8*7!
Question: At a dinner party, 3 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
(A) 2
(B) 10
(C) 24
(D) 32
(E) 120
Rationale: Soln: Since the arrangement is circular and 2 seating arrangements are considered different only when the positions of the people are different relative to each other, we can find the total number of possible seating arrangements, by fixing one person's position and arranging the others.
Thus if one person's position is fixed, the others can be arranged in 2! =2 ways.
Ans is A.
Answer: (A) 2
Question: Of the people who responded to a market survey, 60 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 3 to 1, how many people responded to the survey?
(A) 80
(B) 150
(C) 240
(D) 360
(E) 480
Rationale: Ratio = 3:1 => 3x respondents preferred Brand X and x preferred Brand Y
Since, no. of respondents who preferred Brand X = 60 => 3x=60 => x=20
Hence Total no. of respondents = 60 + 20 = 80
Hence A is the answer.
Answer: (A) 80
Question: A solution of 70 litres contains oil and water in the ratio 9:x. If six litres of water is added to the solution, the ratio becomes 6:4, find the value of x?
(A) 6
(B) 8.5
(C) 9
(D) 6.5
(E) 5
Rationale: Exp. Total new quantity = original sol + water =70+6 =76
New ratio = 6:4, New quantity of oil =6/10*76 = 45.6 Lit,
New quantity of water = 4/10*76 = 30.4 Lit
Water present initially = (30.4-6) = 24.4 Lit
Ratio = 45.6/24.4 =9/x There for x = 4.81 approx 5
Answer: E
Answer: (E) 5
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 54 years now, the son's age 8 years back was?
(A) 12yr
(B) 19yr
(C) 14yr
(D) 10yr
(E) 20yr
Rationale: Let the son's present age be x years
Then, 54-x = x
x = 27
Son's age 8 years back = 27-8= 19years
Answer is B
Answer: (B) 19yr
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'8" tall, which of the following is the median height of the children?
(A) 2'8"
(B) 2'6"
(C) 3'3"
(D) 3'4"
(E) 4'3
Rationale: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'8"+2'8")/2 = 2'6"
Ans:Option A
Answer: (A) 2'8"
Question: Mother,her daughter and her grand child weighs 130 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?
(A) 46
(B) 47
(C) 48
(D) 49
(E) 50
Rationale: mother + daughter + child = 130kg
daughter + child = 60kg
mother = 130 - 60 = 70kg
child = 1/5th of mother = (1/5)*70 = 14kg
So now daughter = 130 -(mother + child) = 130 - (70+14) = 46kg
ANSWER:A
Answer: (A) 46
Question: If 6 (A's capital) = 8 (B's capital) = 14 (C's capital). Then the ratio of their capitals is?
(A) 20:15:16
(B) 20:15:68
(C) 28:21:12
(D) 28:15:11
(E) 28:15:19
Rationale: 6A = 8B = 14 C
A:B:C = 1/6:1/8:1/14
= 28:21:12
Answer: C
Answer: (C) 28:21:12
Question: Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Taking the prices of products in ascending order(already arranged)
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $239
we see that median value is the 6th value as there in total 11 values given
Arithmetic mean = total/number of entries = 1428/11 =129.8181
We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price
as we can clearly see that there is one value between $120 and $129.81, answer is 1 unit
Correct Answer - B
Answer: (B) 1
Question: What is the sum of all remainders obtained when the first 200 natural numbers are divided by 9?
(A) 397
(B) 401
(C) 403
(D) 405
(E) 399
Rationale: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=401.
Answer: B.
Answer: (B) 401
Question: 40 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 6 like all. How many people like apple?
(A) 47
(B) 49
(C) 54
(D) 58
(E) 62
Rationale: orange+mango-apple=7
mango+apple-orange=10
apple=40
orange+mango+apple=6
40+10+6-7=49 like apple
ANSWER:B
Answer: (B) 49
Question: If 20% of a number = 100, then 120% of that number will be?
(A) 20
(B) 120
(C) 360
(D) 600
(E) 820
Rationale: Let the number x. Then,
20% of x = 100
x = (100 * 100)/20 = 500
120% of x = (120/100 * 500) = 600.
ANSWER:D
Answer: (D) 600
Question: A bag contains 5 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
(A) 8/15
(B) 2/5
(C) 3/5
(D) 11/15
(E) 19/39
Rationale: Drawing two balls of same color from five green balls can be done in 5C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 5C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 19/39
ANSWER:E
Answer: (E) 19/39
Question: FOG + FOG + FOG + FOG = 1448.
If F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: given,FOG + FOG + FOG + FOG = 1448
4(FOG)=1448
=>FOG=362
Face value of F is:3
Face value of O is:6
Face value of G is:2
so F+O+G=3+6+2=11
ANSWER:A
Answer: (A) 11
Question: what will be the unit value of 0!*1!*6!-5!?
(A) 4
(B) 3
(C) 0
(D) 1
(E) 2
Rationale: 1*1*5!*6-5!
5!(6-1)
5!*5
4!*5*5
it will be 0 because 5*4 with 0 at unit place so with any no. you multiply who have 0 unit place the product also have 0 at unit place.
answer C
Answer: (C) 0
Question: Find the area of a parallelogram with base 12 cm and height 18 cm.
(A) 200
(B) 216
(C) 345
(D) 244
(E) 242
Rationale: Area of a parallelogram = base * height = 12 * 18 = 216 cm2
Answer: Option B
Answer: (B) 216
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 184 hats in this group, how many of these hats are not blue?
(A) 28
(B) 42
(C) 48
(D) 128
(E) 76
Rationale: Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=184 or 23x=184...here 7x,4x and 12x represent hats of each type
23x=184 so x=8...Blue hats =7*8=56...Not blue will be 184-56=128.
Ans D
Answer: (D) 128
Question: Find the L.C.M of 32,84,126
(A) 2000
(B) 2018
(C) 5032
(D) 1008
(E) 2016
Rationale: 32=2^5 84=2^2*3*7 126=2*3^2*7
L.C.M=2^5*3^2*7=2016
Answer=(E)
Answer: (E) 2016
Question: A hostel had provisions for 250 men for 40 days. If 50 men left the hostel, how long will the food last at the same rate?
(A) 48 days
(B) 50 days
(C) 45 days
(D) 60 days
(E) None of these
Rationale: Explanation :
A hostel had provisions for 250 men for 40 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required numer of days = x days
More men, Less days (Indirect Proportion)
⇒Men250:200}::x:40
⇒250 × 40 = 200x
⇒ 5 × 40 = 4x
⇒ x = 5 × 10 = 50. Answer : Option B
Answer: (B) 50 days
Question: Barbara has 8 shirts and 5 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
(A) 41
(B) 24
(C) 36
(D) 70
(E) 56
Rationale: 8 shirts
9 pants
we can combine 2 shirts with (5-3) pants
2*2=4
we can combine the other shirts (6) with any pants (9)
4*5=20
Thus total :20+4=24ANS:B
Answer: (B) 24
Question: Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?
(A) 8
(B) 9
(C) 6
(D) 4
(E) 1
Rationale: Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.
x(2/75 + 1/45) + (30- x) 2/75 = 1
11x + 180 - 6x = 225 => x = 9
Answer:B
Answer: (B) 9
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) 2000
(B) 2778
(C) 2299
(D) 2778
(E) 2771
Rationale: Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.
Answer:A
Answer: (A) 2000
Question: Of the three-digit integers greater than 600, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A)  90
(B)  82
(C)  80
(D)  75
(E)  36
Rationale: Let the three digit number be represented as X Y Z.
There are 3 cases:
Case I.[ X=Y ]Z is not equal to XY :XXZorYYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 1 way
After XY are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(1)
[example numbers: 774,779,882,993 etc]
Case II.[ X=Z ]Y is not equal to XZ:XYXorZYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Z can be chosen in 1 way
After XZ are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (9 ways) * (1 way) = 27 ....(2)
[example numbers: 747,797,828,939 etc]
Case III.[ Y =Z ]X is not equal to YZ :XYYorXZZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 9 ways
After Y is chosen, Z can have 1 way
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(3)
[example numbers: 744,799,822,933 etc]
Therefore, total numbers of possible digits [sum of Case (1), (2)(3) above] = 27 + 27 + 27 - 1 = 80
One digit is subtracted from total number of possible digits to eliminate one possibility of XYZ = 700 to satisfy the condition that digit > 600.
Answer:(D)
Answer: (D)  75
Question: At a local appliance manufacturing facility, the workers received a 15% hourly pay raise due to extraordinary performance. If one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged, by approximately what percent would he reduce the number of hours that he worked?
(A) 13%
(B) 80%
(C) 20%
(D) 17%
(E) 12%
Rationale: Let's say he works usually 10 hours and earns 100 per hour.
10 * 100 = 1000
10 * 115 = 1150 (this are the new earnings after the raise)
To figure out how much he needs to work with the new salary in order to earn the original 1000:
1000/115 = 8.7
So he can reduce his work by 1.3 hours. Which is >13%.
Answer A
Answer: (A) 13%
Question: X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 32 days. How long will Y take to complete the work?
(A) 10
(B) 40
(C) 15
(D) 18
(E) 20
Rationale: Work done by X in 8days = 8*1/40 = 1/5
Remaining work = 1 - 1/5 = 4/5
4/5 work is done by Y in 32 days
Whole work will be done by Y in 32*5/4 = 40 days
Answer is B
Answer: (B) 40
Question: A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
(A) 288
(B) 236
(C) 350
(D) 299
(E) 266
Rationale: D = 72 * 5/18 = 25 = 500 – 150 = 299.Answer:C
Answer: (C) 350
Question: 8, 24, 12, 36, 18, 54, (....)
(A) 27
(B) 68
(C) 107
(D) 108
(E) 28
Rationale: 8 × 3 = 24
24 ÷ 2 = 12
12 × 3 = 36
36 ÷ 2 = 18
18 × 3 = 54
54 ÷ 2 = 27
Answer is A
Answer: (A) 27
Question: Mixture of milk & water has been kept in two separate bowl. Ratio of milk to water in one of the bowls is 5 : 1 and that in the other bowl 7 : 2. In what ratio the mixtures of these 2 bowl should be added together so that the quantity of milk in the new mixture may become 80%?
(A) 2:3
(B) 3:5
(C) 4:5
(D) 5:7
(E) 6:11
Rationale: Lett. mixtures of the two containers be added together in the ratio of x
= = [ixoox l00%
Since the percentage quantity ofmilk in the new mixture is SO% — so% (45x + 42y) x 5 4 x 54(x y) 225x 210y 216.3E+216y
9x=6y
x:y=2:3
A
Answer: (A) 2:3
Question: If Q is a negative integer, which of the following must be a negative integer?
(A) Q + 1
(B) Q/2+3
(C) Q^4
(D) Q – y
(E) Q^11
Rationale: We need to check each option here:
A. Q + 1
This will depend on the value of Q. Nothing can be said
B. Q/2+3
This will depend on the value of Q. Nothing can be said
C. Q^4
This will always be positive. Even powers of negative numbers are positive and odd powers are negative
D. Q – y
This will depend on the value of Q. Nothing can be said
E. Q^11
This will always be negative. Even powers of negative numbers are positive and odd powers are negative
Correct Option: E
Answer: (E) Q^11
Question: When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?
(A) 1/8
(B) 1/4
(C) 1/3
(D) 3/8
(E) 1/2
Rationale: Winning scenario is if we'll have either three tails (TTT) or three heads (HHH): 1/2*1/2*1/2+1/2*1/2*1/2=1/4.
Answer: B.
Answer: (B) 1/4
Question: Samantha's investment portfolio consists of three stocks: an airline, a bank, and a computer company. In the month of February, the price of the airline's stock rose by 10%, that of the bank decreased by 10% and that of the computer company also decreased by 15%, but the overall value of her portfolio increased. If Samantha owns equal amounts of all three stocks, which of the following could be the initial prices of the three stocks in the order airline, bank, and computer company respectively?
(A) $55, $85, $40
(B) $65, $60, $60
(C) $85, $55, $45
(D) $85, $25, $20
(E) $25, $60, $70
Rationale: Since Samantha owns equal amounts of stocks, the 10% increase alone should set off the 10% and 15% decrease in each of the other two stocks. i.e The stock which increased should have a substantially higher value than the two stocks which decreased. Between B and C, C is obviously the safer bet and is the right answer.
Answer is C.
Answer: (C) $85, $55, $45
Question: A customer pays 70 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
(A) A)$50
(B) B)$60
(C) C)$70
(D) D)$80
(E) E)$90
Rationale: Let x be the original price.
x - 20 = 70
x - 20 + 20 = 70 + 20
x + 0 = 90
x = 90
correct answer is E)$90
Answer: (E) E)$90
Question: 27 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) 33
(B) 66
(C) 88
(D) 100
(E) 281
Rationale: (27 * 8)/30 = (x * 6)/50 => x =60
60 – 27 = 33
Answer: A
Answer: (A) 33
Question: We run a business that rents out canoes and kayaks. A canoe rental costs $15 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $405 in revenue. How many more canoes than kayaks were rented out?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the number of canoes.
Then 2x/3 is the number of kayaks.
15x+(2x/3)*18=405
15x+12x=405
27x=405
x=15 (canoes)
2x/3=10 (kayaks)
There were 15-10 = 5 more canoes rented out.
The answer is A.
Answer: (A) 5
Question: The present age of a father is 3 years more than three times the age of his son.Three years hence,father as age will be 10 years more than twice the age of the son.Find the present age of the father.
(A) 88
(B) 77
(C) 33
(D) 44
(E) 55
Rationale: Explanation:
Let the present age be 'x' years. Then father's present age is 3x+3 years. Three years hence (3x+3)+3=2(x+3)+10 x=10 Hence father's present age = 3x+3 =[ (3 x 10) + 3] = 33 years.
Answer: C
Answer: (C) 33
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for two years?
(A) 29893
(B) 27773
(C) 29989
(D) 28800
(E) 23400
Rationale: Simple interest = (18000 * 2 * 15)/100 = Rs. 5400
Amount = P + I = 18000 + 5400 = Rs. 23400
Answer: E
Answer: (E) 23400
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
(A) 16 2/8%
(B) 16 6/3%
(C) 76 2/3%
(D) 16 2/3%
(E) 96 2/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: (D) 16 2/3%
Question: A family made a down payment of $100
and borrowed the balance on a set of
encyclopedias that cost $400. The
balance with interest was paid in 20
monthly payments of $17.2 each and a
final payment of $3. The amount of
interest paid was what percent of the
amount borrowed?
(A)  6%
(B)  12%
(C)  14%
(D)  15.6%
(E)  20%
Rationale: interest paid = 17.2*20+3 - 300=47
% off the balance = (47/300) * 100 = 15.67%
Answer is D.
Answer: (D)  15.6%
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
(A) (180-x)/2
(B) (x+60)/4
(C) 4800/x+100
(D) 600/(115-x)
(E) 12,000/(x+200)
Rationale: total distance =100 ;total time = T
t1 = x/30 t2 = 100-x /60
T =t1+t2 = x/30 + 100-x/60 = (60x + 3000- 30x)/1800
= (30x+3000)/1800
= x +100 / 60
av speed = 100*60/x+100 = 4800/x+100
C
Answer: (C) 4800/x+100
Question: A train 1000 m long passed a pole in 20 sec. How long will it take to pass a platform 500 m long?
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: Speed = 1000/20 = 50 m/sec.
Required time = (1000 + 500)/50
= 30 sec.
Answer:E
Answer: (E) 30
Question: The average of five results is 48 and that of the first four is 45. The fifth result is?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: 5 * 48 – 4 * 45 = 60
ANSWER:B
Answer: (B) 60
Question: In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 4.25 sec
(C) 3.75 sec
(D) 12.5 sec
(E) 6 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 150/40 = 3.75 sec.
ANSWER:C
Answer: (C) 3.75 sec
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 298 m
(B) 268 m
(C) 500 m
(D) 267 m
(E) 181 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer: C
Answer: (C) 500 m
Question: A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
(A) 107
(B) 117
(C) 127
(D) 137
(E) 147
Rationale: Let us calculate both the length and width of the room in centimeters.
Length = 6 meters and 24 centimeters = 624 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48
Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117
Answer: B
Answer: (B) 117
Question: If xy = 5 and x^2 + y^2 = 15, then x/y + y/x =
(A) 5
(B) 3 1/7
(C) 5 1/3
(D) 7
(E) 60
Rationale: We can make simplifying of question and get it in view: (x^2 + y^2) / xy and as we know the meaning of this parts:
x^2 + y^2 = 15
xy = 5
we can calculate the answer 15/5 -> 5 so answer is A
Answer: (A) 5
Question: Missing number in the series
4 9 20 43 90 185 376 759?
(A) 1750
(B) 1850
(C) 1900
(D) 1950
(E) 1526
Rationale: 4*2+1=9
9*2+2=20
20*2+3=43
43*2+4=90
90*2+5=185
185*2+6=376
376*2+7=759
759*2+8=1526
ANSWER:E
Answer: (E) 1526
Question: A certain school principal must choose 5 students to attend a field trip out of a group of 12 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?
(A) 1,260
(B) 2,520
(C) 15,840
(D) 6,020
(E) 10,080
Rationale: 5 students can be selected out of 12 students in 12C5 ways.
out of the remaining 5 students,Note taker can be chosen in 5 ways.
Finally only 4 students remain from which we can choose a treasurer in 4 ways.
Total number of ways = 792 * 5 *4 = 15840
correct answer - C
Answer: (C) 15,840
Question: In doing a division of a question with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is
(A) 0
(B) 12
(C) 13
(D) 20
(E) None
Rationale: Sol.
Dividend = (12 x 35) = 420.
Now, dividend = 420 and divisor = 21.
∴ Correct quotient = 420 / 21 = 20.
Answer D
Answer: (D) 20