mathewhe/aqua_rat huggingface dataset:
Question: A man sells a horse for Rs.140 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 420
(B) 299
(C) 277
(D) 860
(E) 771
Rationale: CP = SP + 1CP = SP - g
140 + x = 980 - 2x
3x = 840=> x = 280
CP = 280 + 140 = 420
Answer: A
Answer: (A) 420
Question: A student travels from his house to school at 10 km/hr and reaches school 1 hour late. The next day he travels 12 km/hr and reaches school 1 hour early. What is the distance between his house and the school?
(A) 100
(B) 105
(C) 110
(D) 115
(E) 120
Rationale: Let x be the distance from his house to the school.
x/10 = x/12 + 2
6x = 5x + 120
x = 120 km
The answer is E.
Answer: (E) 120
Question: A box contains 3 red balls and 4 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
(A) 7/4
(B) 1/2
(C) 1/2
(D) 5/8
(E) 2/3
Rationale: My complicated version of your simple approach
Let the 5 black balls be BBBBB and 3 Red Balls be RRR
They can be arranged in 8 slots _ _ _ _ _ _ _ _
in (7!)/ (4!x3!)
If the fourth slot is Black ball then the arrangement will be to fill
_ _ _ B _ _ _ _
we have 7 slots and 3 Black (BBB) and 3 Red (RRR)
They can be arranged in (6!)/ (3!x3!)
Hence required probability = [(7!)/ (4!x3!)]/[(6!)/ (3!x3!)]
Ans = 7/4
A
Answer: (A) 7/4
Question: A sum fetched total simple interest of 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
(A) 8925
(B) 8032.5
(C) 4462.5
(D) 8900
(E) None of these
Rationale: Let the sums be P.
Now, 45% of P = 4016.25
or, P = 8925
Answer A
Answer: (A) 8925
Question: When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $112.70, what was the total value of the item?
(A) $2420
(B) $2610
(C) $2860
(D) $3050
(E) $3270
Rationale: Let x be the value of the item.
0.07*(x-1000) = 112.70
x = 2610
The answer is B.
Answer: (B) $2610
Question: A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?
(A) 1/720
(B) 1/80
(C) 1/10
(D) 1/9
(E) 1/5
Rationale: Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/10+1/10=2/10.
Answer: E.
Answer: (E) 1/5
Question: 121, 169, 225, 289, 361, ?, F ind the missing number(?).
(A) 529
(B) 441
(C) 390
(D) 411
(E) 201
Rationale: The series consists of squares of consecutive ODD numbers .
Answer : B.
Answer: (B) 441
Question: On a two-dimensional coordinate plane, the line z = x^2 - x^3 touches the x-axis in how many places?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: Apparently it's z = x^2 - x^3 instead of z = x^2 - z^3.
In this case: the x-intercept is the value(s) of x for z = 0.
0 = x^2 - x^3;
0 = x^2(1 - x);
x = 0 or x = 1.
Answer: C.
Answer: (C)  2
Question: . In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 80 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A)  50%
(B)  53%
(C)  54%
(D)  55%
(E)  56%
Rationale: Registered voters = 100
D = 60
R = 40
80% of D ( 60) = 48
20% of R ( 40 ) = 8
Total voter% of registered voters = 56 / 100
56% Ans E
Answer: (E)  56%
Question: A string of 50 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.05, what is the probability that the string of light bulbs will fail during the time period T?
(A) 0.05
(B) (0.05)^50
(C) 1 - (0.96)^50
(D) 1 - (0.95)^50
(E) (0.95)^50
Rationale: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 50 light bulbs fails, since the probability of each light bulb not to fail is 1-0.05=0.95 the the probability that none of the 50 light bulbs fails is 0.95^50.
Hence, the probability that at least one light bulb fails is 1-0.95^50.
Answer: D.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 50, then according to your logic the probability that the string of light bulbs will fail would be 100*0.05=5, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: (D) 1 - (0.95)^50
Question: You own thirteen pairs of socks, all different, and all of the socks are individually jumbled in
a drawer. One morning you rummage through the drawer and continue to pull out socks until
you have a matching pair. How many socks must you pull out to guarantee having a matching
pair?
(A) 3
(B) 12
(C) 13
(D) 14
(E) 25
Rationale: You might be unlucky and have the first thirteen socks all different, but then the 14th
has to match one of them.
correct answer D
Answer: (D) 14
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 188
(B) 786
(C) 991
(D) 860
(E) 121
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Answer: (D) 860
Question: A new savings account offers 6 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?
(A) $80.00
(B) $84.40
(C) $360.00
(D) $6,360.00
(E) $6,365.40
Rationale: Solution -
At the end of the first 6 months, the interest earned is (1/2)*6000*(6/100) = 180. (6 months is 1/2 in the equation since 6% is a yearly rate, not for six months).
Since the interest is compounded, the second six months of the year is getting interest on original and first six months interest i.e.,6180.
The interest earned during the final 6 months of the year is (1/2)*6180*(6/100) = 185.4
The total balance at the end of the year is 6000+180+185.4=6365.4
Answer: E
Answer: (E) $6,365.40
Question: A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 30 meters apart,then at what speed is the train traveling?
(A) 100km/hr
(B) 110km/hr
(C) 50km/hr
(D) 150km/hr
(E) 90km/hr
Rationale: Number of gaps between 51 telephone posts = 50
Distance traveled in 1 minute = 50*30 = 1500m = 1.5km
Speed = 60*1.5=900km/hr
Answer is E
Answer: (E) 90km/hr
Question: If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 16?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 9/16
(E) 3/4
Rationale: I get 5/8 as well
1 to 96 inclusive means we have 48 odd and 48 even integers
E O E / 16 = Integer, therefore we have 48 / 96 numbers divisible by 8
O E O / 16 = Not Integer
We cannot forget multiples of 16 from 1 to 96
We have 6 numbers that are multiple of 16
Therefore, 48/96 + 6/96 = 54/96 = 9/16
answer : D
Answer: (D) 9/16
Question: Out of three consecutive odd numbers eleven times the first number is equal to addition of thrice the third number and adding 8 to five times the second . What is the first number?
(A) 10
(B) 6
(C) 11
(D) 8
(E) 9
Rationale: Description :
=> 11x=5(x+2)+8+3(x+4)
=> 11x=8x+30
=> 3x=30
X=10
Answer A
Answer: (A) 10
Question: In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a three or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
(A) 1/3
(B) 4/9
(C) 5/9
(D) 2/3
(E) 3/4
Rationale: We're looking for the number of outcomes that include AT LEAST a 1 or a 3.
#getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6
#getting a one in 2nd die {(2,1), ...(5,1),(6,1) } = 4 [exclude 1,1 and 3,1] since it will be counted twice
#getting a three in 1st die {(3,1), (3,2), ...(3,6) }= 6
#getting a three in 1st die {(2,3), (4,3), ...(6,3) } = 4 [exclude 1,3 and 3,3] since it will be counted twice
Total possibities = 20
Probability of rolling at least a 1 or a 3 on two dice: 20/36 = 5/9
C
Answer: (C) 5/9
Question: What will come in place of the question mark (?) in the following questions?
18.2% of 890 = ?
(A) 161.98
(B) 234.98
(C) 642.98
(D) 141.98
(E) 211.98
Rationale: A
161.98
? = (890 * 18.2)/100
= 161.98
Answer: (A) 161.98
Question: Two employees X and Y are paid a total of Rs. 506 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.250
(B) s.280
(C) s.290
(D) s.299
(E) s.230
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 506
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 506
⇒ y[12/10 + 1] = 506
⇒ 22y/10 = 506
⇒ 22y = 5060
⇒ y = 5060/22 = 460/2 = Rs.230
E
Answer: (E) s.230
Question: In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
(A) 16
(B) 17
(C) 18
(D) 19
(E) 14
Rationale: Let there were x teams participating in the games, then total number of matches,
nC2 = 153.
On solving we get,
=> n =−17 and n =18.
It cannot be negative so,
n = 18 is the answer.
OPTION:C
Answer: (C) 18
Question: Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra?
(A) Rs.7000
(B) Rs.8000
(C) Rs.8500
(D) Rs.8600
(E) Rs.8700
Rationale: The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1.
:. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000.
B)
Answer: (B) Rs.8000
Question: In a certain circle there are 10 points. What is the number of the triangles connecting 4 points of the 10 points?
(A) 80
(B) 96
(C) 108
(D) 120
(E) 210
Rationale: IMO : E
HERE we have to select 4 points out of 10 points. Order is not important
So the answer will be 10c4 = 210
Answer: (E) 210
Question: Jim and Reneey will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneey have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?
(A) 5/6
(B) 2/3
(C) 1/2
(D) 5/12
(E) 1/3
Rationale: 1/3
probability of jim winning is basically the sum of three probabilities:
probability of jim picking rock and reneey picking scissors = 1/3*1/3 = 1/9
probability of jim picking scissors and reneey picking paper = 1/3*1/3=1/9
probability of jim picking paper and reneey picking rock = 1/3*1/3=1/9
1/9 + 1/9 + 1/9 = 3/9 = 1/3=E
Answer: (E) 1/3
Question: John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/5 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?
(A) 59
(B) 65
(C) 70
(D) 77
(E) 98
Rationale: Rakesh : Rahul : Ranjan : Rohit = 1 / 5 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 5 x 60 ) = 12
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 12 x + 20 x + 15 x + 12 x) = 59 x.
For minimum number of pencils x = 1 .
The person should have at least 59 pencils.
A)
Answer: (A) 59
Question: A research team is to consist of 3 scientists from Company A and 3 scientists from Company B. If the pool of available scientists from Company A is 5 and the pool of available scientists from Company B is 4 scientists, how many different research teams are possible?
(A) 84
(B) 40
(C) 30
(D) 20
(E) 12
Rationale: C35∗C34=40
Answer: B.
Answer: (B) 40
Question: The product of all the prime numbers less than 22 is closest to which of the following powers of 10?
(A) 10^9
(B) 10^8
(C) 1*10^7
(D) 10^6
(E) 10^5
Rationale: Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19
=2.1x10^2*1.3*1.7*1.9
=9.69* 10^6
=1*10^7
C
Answer: (C) 1*10^7
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 4^a and y = 3^b, which of the following is a possible units digit of xy?
(A) 1
(B) 8
(C) 5
(D) 7
(E) 9
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=4
a=2; X=16
a=3; X=64........ Units digit repeat in a cycle of 4,6,4,6......
Similarly, Finding all values of Y for positive values ofb
b=1; Y=3
b=2; Y= 9
b=3; Y= 27
b=4; Y=81
b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=4 and Y=3: Units digit of XY = 12
When X=4 and Y=9: Units digit of XY = 36
When X=4 and Y=7: Units digit of XY = 28
When X=4 and Y=1: Units digit of XY = 4
Only four possibilities for Units digit of XY i.e. 4, 2, 8 and 6.
Only 8 is given in answer choices, therefore answer is B
Answer: (B) 8
Question: What is the remainder if 7^12 is divided by 100?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 7^16 can be written as (7^4)^3
If we divide 7^4 by 100 the reminder is 1
So, (7^4)^3 by 100, the reminder is 1^3 = 1
Answer : A
Answer: (A) 1
Question: A retail item is offered at a discount of d percent (where d > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of d, would result in the same final price?
(A) d+5/1.05
(B) d/1.05 +5
(C) 1.05d-5
(D) d-5/1.05
(E) 1.05(p – 5)
Rationale: Let x be the price of the item.
Final price after discount and sales tax = x * (1 - d/100) * 1.05
Let e be the percent discount which would result in the same final price.
Then,
x * (1 - d/100) * 1.05 = x * (1 - e/100)
=> 1.05 - 1.05d/100 = 1 - e/100
=> e/100 = 1.05d/100 - .05
=> e = 1.05d - 5
Hence ,option C is correct.
Answer: (C) 1.05d-5
Question: If a fair die is rolled once, what is the probability that a 3 occurs on at least one roll?
(A) 25/36
(B) 125/216
(C) 1/6
(D) 1/36
(E) 5/6
Rationale: Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)
Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6) = 1-5/6 = 1/6
5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.
C is thus the correct answer.
Answer: (C) 1/6
Question: When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?
(A) 40
(B) 41
(C) 42
(D) 43
(E) 45
Rationale: Let the age of Usha is 3x then Nisha is x and Asha is 25
Also Usha 34, Nisha y, and Asha 2y.
We know that 3x - 34 = x - 2y = 25 - 2y
Solving above three equations we get x = 9, y = 16
Their ages are 34, 16, 32. whose sum = 82. So after 18 years their ages will be equal to 100. So Usha age is 34 + 6 = 40
Answer:A
Answer: (A) 40
Question: For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 80 of this series?
(A) 8990
(B) 9380
(C) 9630
(D) 9960
(E) 10,240
Rationale: Each term of the series has the form (n+n+1+n+2) = 3n+3
Since the series goes from 1 to 80, the sum of the series is:
3(1+2+...+80) + 80(3) =
3(80)(81)/2 + 80(3) =
120*81 + 240 = 9960
The answer is D.
Answer: (D) 9960
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is "frozen" if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently six spaces behind player B, what is the probability that player B will be frozen after player A rolls?
(A) 1/12
(B) 5/36
(C) 1/6
(D) 1/3
(E) 17/36
Rationale: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 6 (as A is 6 spaces behind B) = 5 ( (1,5), (2,4), (3,3), (4,2), (5,1) )
So, the probability = 5/36 (Option B)
Answer: (B) 5/36
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 8 cm above the ground, what is the radius of the other ball?
(A) 12 cm
(B) 16 cm
(C) 18 cm
(D) 20 cm
(E) none of the these
Rationale: similar triangle properties..
2/r+6 = 6/r-6
giving r = 12.
Answer: A
Answer: (A) 12 cm
Question: What is the difference between the place value and the face value of 9 in the numeral 296827?
(A) None of these
(B) 89993
(C) 89991
(D) 89994
(E) 89995
Rationale: Explanation:
Place value of 9 = 90000
Face value of 9 = 9
Difference = 9000 - 9 = 89991
Answer: C
Answer: (C) 89991
Question: A whale goes on a feeding frenzy that lasts for 5 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the third hour?
(A) 38
(B) 47
(C) 50
(D) 53
(E) 93
Rationale: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is 450/5 = 90, so the median is also 90, and that is the amount eaten in the 2nd hour. We need to add 3 to find the total eaten in the next hour, so the answer is 93
option E
Answer: (E) 93
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 250 per month. What is his monthly salary?
(A) 5000
(B) 2999
(C) 2878
(D) 6250
(E) 2771
Rationale: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 â€“ 96 =Rs. 4
100 ------ 4
? --------- 250 => 6250
Answer: D
Answer: (D) 6250
Question: If the average (arithmetic mean) of seven consecutive integers is k - 2, then the product of the greatest and least integer is
(A) k2 - 9
(B) k2 - 2k + 1
(C) k2 - 4k - 5
(D) k2 + 6k + 9
(E) k2 + 4k - 12
Rationale: n = smallest number
n+6 = largest number
(n + n + 6)/2 = k - 2
=> (2n+6)/2 = k - 2
=> n + 3 = k - 2
=> n = k - 5
So Product of n and n+6 = (k-5)(k+1)
= k^2 - 5k + k - 5
= k^2 - 4k - 5
Answer - C
Answer: (C) k2 - 4k - 5
Question: Find the odd man out. 3, 8, 18, 38, 78, 158, 316
(A) 38
(B) 158
(C) 316
(D) 8
(E) None of these
Rationale: Explanation :
3
3 × 2 + 2 = 8
8 × 2 + 2 = 18
18 × 2 + 2 = 38
38 × 2 + 2 = 78
78 × 2 + 2 = 158
158 × 2 + 2 = 318
Hence, 316 is wrong and 318 should have come in place of that. Answer : Option C
Answer: (C) 316
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three (vice presidents)/VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
(A) 0.5
(B) 0.6
(C) 0.7
(D) 0.49
(E) 0.8
Rationale: probability of adams approval = 0.7
baker approval =0.5
corfu approval=0.4
proabability of approval is must adam approval and atleast one approval
= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+
adam approval*baker not approval*coffu approval( atleast one remaining approval
= 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4
=0.14+0.21+0.14
=0.49
D
Answer: (D) 0.49
Question: A train 130 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 4
(B) 7
(C) 5
(D) 9
(E) 8
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [130* 3/55] sec = 7 sec
ANSWER:B
Answer: (B) 7
Question: An auction house charges a commission of 25% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?
(A) $115,000
(B) $165,000
(C) $215,000
(D) $240,000
(E) $365,000
Rationale: Say the price of the house was $x, then 0.25*50,000+0.1*(x-50,000)=24,000 --> x=$165,000 (25% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).
Answer: B.
Answer: (B) $165,000
Question: A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ?
(A) 40.4 sec
(B) 40.5 sec
(C) 50.4 sec
(D) 50.5 sec
(E) 60.4
Rationale: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 770 m
Time = Distance / Speed
= 770 x 18 / (5 x 55)
= 50.4 sec
correct Answer: option a
Answer: (A) 40.4 sec
Question: A hall 36m long and 15m broad is to be paved with stones, each measuring 2dm by 5 dm. The number of stones required is:
(A) 180
(B) 1800
(C) 5400
(D) 18000
(E) 1.8
Rationale: Area of the hall= 3600*1500
Area of each stone= (20*50)
Therefore, number of stones= (3600*1500/ 20*50)= 5400
ANSWER:C
Answer: (C) 5400
Question: A boy has seven trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 88
(B) 98
(C) 106
(D) 108
(E) 84
Rationale: Explanation:
The boy can select one trouser in seven ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 7 * 12 = 84 ways
E)
Answer: (E) 84
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:5
(C) 1:9
(D) 1:3
(E) 1:1
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Answer: (A) 1:2
Question: On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars abroad the ship. If 40 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship's passengers held round-trip tickets?
(A) 33.3%
(B) 40%
(C) 50%
(D) 60%
(E) 66.6%
Rationale: 0.20P = RT + C
0.4(RT) = no C
=> 0.60(RT) had C
0.20P = 0.60(RT)
RT/P = 1/3=33%
Answer - A
Answer: (A) 33.3%