RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A certain pair of used shoes can be repaired for $11.50 and will last for 1 year. A pair of the same kind of shoes can be purchased new for $28.00 and will last for 2 years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?
A.20.8
B.21.46
C.21.74
D.22.3
Answer: C.21.74
Explanation: 1) Cost of repairing = 11.5 ( for one year ), Therefore for 2 years it would be$ 23.
2) Cost of new pair which will last for 2 years is$ 28.
Percentage change formula =( Final value - Initial value ) / ( Initial Value ) * 100. In this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe.
I.e ( 28 - 23 ) / ( 23 ) * 100 = 21.74 %.
Ans is C
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 1 kmph, then the speed in downstream is?
A.16
B.77
C.20
D.99
Answer: A.16
Explanation: M = 15
S = 1
DS = 15 + 1 = 16
Answer: A
Question: Both the roots of the equation
(x - b)(x - c) + (x - b)(x - a) + (x - a)(x - b) = 0
A.dependent on a, b, c
B.always non real
C.always real
D.rational
Answer: C.always real
Explanation: Sol.(c) The equation is
3x2 - 2(a + b + c)x + (bc + ca + ab) = 0
The discriminant
D = 4(a + b + c)2 - 4.3.(bc + ca + ab)
= 4[a2 + b2 + c2 - ab - bc - ca]
= 2[(a2 - 2ab + b2) + (b2 - 2bc + c2) + (c2 - 2ca + a2)]
= 2[(a - b)2 + (b - c)2 + (c - a)2] ≥ 0
∴ Roots are always real.
Answer C
Question: Jaya can do a work in 10 days while Mahe can do the same work in 15days. Both of them finish the work together and get $300. What is the share of Jaya?
A.$100
B.$50
C.$150
D.$180
Answer: D.$180
Explanation: Jaya's wages: Mahe's wages = 1/10 : 1/15 = 15:10 = 3:2
Jaya's share = 300*3/5 = $180
Answer is D
Question: A departmental store has 4 managers and 16 associates. The 4 managers have an average salary of $900. The 16 associates have an average salary of $10,000. What is the average salary for the departmental store?
A.$8180
B.$9190
C.$4140
D.$5150
Answer: A.$8180
Explanation: Number of managers is 4
Their average salary is $900
Number of associates is 16
Their average salary is $10,000
Total salary of managers is 4*900=$3600
Total salary of associates is 16*10,000=$160,000
Total salary for the departmental store is 160,000+3600=163600
Average salary for the departmental store is 163600/20=8180
Answer is A
Question: Ten years ago A was half of B’s Age. If ratio of their present ages is 3:4 then what is the total of their present ages?
A.30 years
B.08 years
C.35 years
D.20 years
Answer: C.35 years
Explanation: present age of A= 3x
present age of B= 4x
10 years ago A was half of B's age
3x-10=1/2(4x-10)
2x=10
x=5
total of their present age
A=3x=3*5=15
B=4x=4*5=20
toatal present age=35yrs
ANSWER:C
Question: There are two containers on a table. A and B. A is half full of wine, while B,which is twice A's size, is one quarter full of wine. Both containers are filled with water and the contents are poured into a third container C. What portion of container C's mixture is wine?
A.11.33%
B.22.33%
C.33.33%
D.44.33%
Answer: C.33.33%
Explanation: Let the size of container A is "x"
then B's size ll be "2x"
A is half full of wine -- >x/2
So remaining "x/2" of A contains water
B is quarter full of win --> 2x/4 --> x/2
So remaining ==> 2x - x/2 = 3x/2
3x/2 of B contains water
Totally C has A's content + B's Content = x + 2x =3x
Wine portion in C = x/2 of "A" + x/2 of "B"
==> x portion of wine
Water portion in C = x/2 of "A" + 3x/2 of "B"
==> 4x/2 ==> 2x portion of water
So portion of wine in C is
x/3x =1/3 portion of wine
if v expressed in %
1/3 * 100 = 33.33%
ANSWER:C
Question: Fill in the missing number:
18 14 12 11 10.5 ?
A.10.1
B.10.4
C.10.2
D.10.25
Answer: D.10.25
Explanation: D
10.25
Divide each number by 2 and then add 5 to it.
Question: What is the number of 7-element subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9}
for which the sum of those 7 elements is a multiple of 3 ?
A.10
B.11
C.12
D.13
Answer: C.12
Explanation: We describe 2 solutions. Let S = {1, 2, . . . , 9}. Observe that the sum of the elements of S
is divisible by 3. So the problem is the same as asking for the number of ways that 2 elements
of S can be chosen so that their sum is divisible by 3 (the other 7 elements of S correspond to a
7-element set as in the problem). Choosing 2 elements of S with sum divisible by 3 corresponds
to either choosing 2 numbers divisible by 3 (which can be done in 3 ways) or choosing 1 number
that is one more than a multiple of 3 and 1 number that is one less than a multiple of 3 (which can
be done in 3 · 3 = 9 ways). Hence, the answer is 3 + 9 = 12.
correct answer C
Question: For what value of x, is |x – 3| + |x + 1| + |x| = 10?
A.0
B.3
C.-3
D.4
Answer: D.4
Explanation: There are 3 transition points: -1, 0, 3
When x > 3,
|x−3|+|x+1|+|x|=10|
x−3+x+1+x=10
x = 4
Satisfies
When 0 < x < 3
|x−3|+|x+1|+|x|=10
−(x−3)+(x+1)+x=10
x = 6 (Not possible since 0 < x < 3)
When -1 < x < 0
|x−3|+|x+1|+|x|=10
−(x−3)+−(x+1)+x=10
x = -8 (Not possible since -1 < x < 0)
When x < -1
|x−3|+|x+1|+|x|=10
-(x - 3) - (x+1) - x = 10
x = -8/3
Satisfies
ANSWER:D
Question: A train 150m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
A.75kmph
B.85kmph
C.95kmph
D.105kmph
Answer: B.85kmph
Explanation: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
150/[(x+5)*5/18] = 6
30(x+5) = 2700
x = 85kmph
Answer is B
Question: What number is missing?
27, 54, ?, 108, 135, 162, 189, 216
A.81
B.95
C.104
D.137
Answer: A.81
Explanation: A
81
Add 27 each time.
Question: A ferry can transport 50 tons of vehicles. Automobiles range in weight from 1,600 to 3,200 pounds. What is the greatest number of automobiles that can be loaded onto the ferry?
A.23
B.41
C.48
D.62
Answer: D.62
Explanation: to get maximum vehicles we must take into consideration the minimum weight i.e 1600 pounds here
since , 1 ton = 2000 pounds
50 tons will be 100,000 pounds
from the answer choices:
let max number of vehicles be 62
total weight will be = 62*1600 = 99200 pounds , which is lesser than the maximum weight allowed .
Ans: D
Question: The average of first 10 natural numbers is?
A.9:3
B.5.5
C.2:2
D.5.2
Answer: B.5.5
Explanation: Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
Answer: B
Question: The sector of a circle has radius of 28 cm and central angle 135o. Find its perimeter?
A.122 cm
B.92.2 cm
C.28.9 cm
D.29.2 cm
Answer: A.122 cm
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 28) + 2(28)
= 66 + 56 = 122 cm
Answer:A
Question: In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling price was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $5,500. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?
A.1. $15,600
B.2. $15,750
C.3. $17,500
D.4. $18,100
Answer: C.3. $17,500
Explanation: Edited the question as there was a typo.
Range = Highest Value - Lowest Value.
Range in May was 15,000 and the lowest price in May was 4,500, thus the highest price in May was 15,000+4,500=19,500.
Range in June was 16,500 and the lowest price in June was 5,500, thus the highest price in June was 16,500+5,500=22,000.
Lowest price of a car in May-June was 4,500 (May) and the highest price of a car in May-June was 22,000, thus the range for May-June is 22,000-4,500=17,500.
Answer: C.
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.22
B.27
C.48
D.99
Answer: C.48
Explanation: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer: C
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
A.5568
B.6369
C.5460
D.5635
Answer: C.5460
Explanation: 5000 * 104/100 * 105/100
=> 5460
Answer:C
Question: What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, 216, x
A.24
B.28
C.36
D.42
Answer: C.36
Explanation: Go on dividing by 6 to the next number
C)
Question: Two trains are moving in opposite direction @ 60 kmph and 90 kmph.Their lengths are 1.10 km and 0.9 km respectively.The time taken by the slower train to cross the faster train in seconds is
A.36
B.45
C.48
D.49
Answer: C.48
Explanation: R.S = (60+90)kmph => (150*5/18)m/sec => (125/3)m/sec
Distance covered = (1.10 + 0.9) km = (2*1000) = 2000 m.
Required time = (2000 * 3/125) = 48sec.
ANSWER:C
Question: In a certain city, 70 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 30 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.65%
B.52%
C.85%
D.69%
Answer: A.65%
Explanation: Say there are total of 100 registered voters in that city. Thus 70 are Democrats and 30 are Republicans.
70*0.80=56 Democrats are expected to vote for Candidate A;
30*0.30=9 Republicans are expected to vote for Candidate A.
Thus total of 56+9=65 registered voters are expected to vote for Candidate A, which is 65% of the total number of registered voters.
Answer: A
Question: If X = the product of seven distinct prime numbers, how many factors does X have besides 1 and itself?
A.108
B.114
C.120
D.126
Answer: D.126
Explanation: Since X has 7 distinct prime factors, X has a total of 2^7 = 128 factors.
Besides 1 and itself, X has 126 factors.
The answer is D.
Question: If k^3 is divisible by 336, what is the least possible value of integer k?
A.56
B.70
C.84
D.96
Answer: C.84
Explanation: k^3 = 336*x = 2^4*3*7*x
The factors of k must at minimum include 2^2*3*7 = 84.
The answer is C.
Question: Set #1 = {A, B, C, D, E}
Set #2 = {K, L, M, N, O}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
A.13/6
B.13/5
C.13/25
D.2/3
Answer: C.13/25
Explanation: So Not a vowel in Set-1 : 3/5
And not a vowel in Ser-2:4/5
Now,
3/5∗4/5=12/25
This is for not a vowel.
Then for at least one vowel will be = 1−12/25=13/25
Answer will be C.
Question: 3 boys and 7 girls can complete John work in 10 days. 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
A.20 days
B.30 days
C.40 days
D.60 days
Answer: C.40 days
Explanation: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Question: Which of the following CANNOT be a value of 7/(x–7)?
A.-1
B.-1/2
C.0
D.2
Answer: C.0
Explanation: The question doesn't ask for the value of x here, but for the possible results of the equation.
If 7/(x-7) = 0, then the numerator must be 0. But since the numerator is 7, the fraction can not be equal to 0.
The answer is C.
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
A.15
B.88
C.44
D.54
Answer: B.88
Explanation: Let the average after 7th inning = x
Then average after 16th inning = x - 3
16(x-3)+87 = 17x
x = 87 - 48 = 39
ANSWER=B
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
A.100
B.110
C.120
D.134
Answer: C.120
Explanation: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Question: If positive integer k is divided by 8, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a prime number
III. k is divisible by 4
A.None
B.I
C.II
D.III
Answer: A.None
Explanation: k = 8m+2 = 2(4m+1)
I. k + m = 2(4m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even
Ans: none of the above
Question: If the difference between the compound interest & simple interest of a certain sum of money is
Rs.72 at 12% p.a. per two year. Find the sum(in Rs.)?
A.200/15
B.200/17
C.220/17
D.240/17
Answer: B.200/17
Explanation: 200/17
C.I=A-P
A=p(1+12/100)^2
S.I=p*2*12/100
C.I-S.I=72 given
substitute and solve
p=200/17
ANSWER:B
Question: What number has a 5:1 ratio to the number 8?
A.22
B.40
C.88
D.52
Answer: B.40
Explanation: 5:1 = x: 8
x = 40
Answer: B
Question: Which of the following is equal to 2^k*7^(k-1)?
A.2*14^(k-1)
B.7*14^(k-1)
C.14^k
D.2*14^k
Answer: A.2*14^(k-1)
Explanation: 2^k*7^(k-1) = 2*2^(k-1)*7^(k-1) = 2*14^(k-1)
The answer is A.
Question: What distance will be covered by a bus moving at 126 kmph in 10 seconds?
A.287
B.600
C.350
D.276
Answer: C.350
Explanation: 126 kmph = 126 * 5/18
= 35 mps
D = Speed * time = 35 * 10
= 350 m.
Answer:C
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 3 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?
A.A)5
B.B)6
C.C)8
D.D)9
Answer: D.D)9
Explanation: Relative speed = 3 + 3 = 6 rounds per hour.
So, they cross each other 6 times in an hour and 3 times in half an hour.
Hence, they cross each other 9 times before 9.30 a.m.
ANSWER:D
Question: A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?
A.17
B.23
C.75
D.77
Answer: B.23
Explanation: Let the number of apples= 100
sold 60% = 60 apples...remaining =40
Thrown away 15%= 6 apples
Remaining =40-6=34
sold 50 % of remaining = 34/2=17
Remaining thrown away = 17 apples
Total thrown away =6+17=23
Percentage thrown = 23/100=23%
Answer: B
Question: The value of 1/(1-y) + 1/(1+y) + 2/(1+y^2) + 4/(1+y^4)
A.8/(1-y^8)
B.4x/(1+y^2)
C.4/(1-y^6)
D.4/(1+y^4)
Answer: A.8/(1-y^8)
Explanation: Highlighted part has mistake as the exponent of y must be 4 in last term
CORRECT QUESTION ISThe value of 1/(1-y) + 1/(1+y) + 2/(1+y^2) + 4/(1+y^4) = ?
Solution is as mentioned below...
one more way that could get the answer in the type of eqn and choices given is to substitute some value for y...
0 would be better as the eq has constant term free of term 'y'..
the Eq gives us 8 as the ans , as also only choice A..
Question: The average of 9 numbers is 7 and the average of 7 other numbers is 11. What is the average of all 16 numbers?
A.9
B.8 3/4
C.7 7⁄8
D.7 1⁄2
Answer: B.8 3/4
Explanation: The average of 9 numbers is 7....
The sum of those numbers is (9)(7) = 63.
The average of 7 other numbers is 11....
The sum of those numbers is (7)(11) = 77
The sum of ALL 16 numbers is 63+77 = 140. The average of those numbers is 140/16 = 35/4 = 8 3/4.
Final Answer:
[Reveal]Spoiler:
B
Question: What is the sum of all the multiples of 10 between 0 and 100?
A.500
B.620
C.550
D.340
Answer: C.550
Explanation: The multiples of 10 between 0 and 100 are 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100. If these are all added together, the result is 550.
Final Answer:
C
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
A.16 2/8%
B.16 5/3%
C.10 2/3%
D.16 2/3%
Answer: D.16 2/3%
Explanation: 600 ---- 100
100 ---- ? => 16 2/3%
Answer:D
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 5 minutes, what part of the cistern will be emptied?
A.4/9
B.5/18
C.4/2
D.4/8
Answer: B.5/18
Explanation: 2/3 ---- 12
? ----- 5 ==> 5/18
Answer: B
Question: In the manufacture of a certain product, 7 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
A.0.125%
B.0.28%
C.0.8%
D.1.25%
Answer: B.0.28%
Explanation: Percent of defective produced = 7%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(7/100)*100%
= (28/10000)*100%
= (28/100)%
= .28 %
Answer B
Question: A grocer purchased 80 kg of rice at Rs. 13.50 per kg and mixed it with 120 kg rice at Rs. 16 per kg. At what rate per kg should he sell the mixture to gain 16%?
A.Rs. 19
B.Rs. 20.5
C.Rs. 17.4
D.Rs. 21.6
Answer: C.Rs. 17.4
Explanation: C.P OF 200 kg of mix = Rs.[ 80*13.50+120*16 ] =Rs.3000
S.P =116% of Rs.3000 = Rs. 116/100*3000 = 3480
Rate of S .P of the mixture = Rs. [ 3480/200] per kg
= Rs. 17.40 per kg
ANSWER:C
Question: Three coins are tossed. What is the probability of getting at most two tails
A.4/8
B.7/8
C.6/8
D.9/8
Answer: B.7/8
Explanation: Since three coins are tossed, sample space = 8
Getting at most two tails=7
p(E) =7/8
ANSWER:B
Question: Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?
A.Rs 870
B.Rs 880
C.Rs 890
D.Rs 900
Answer: C.Rs 890
Explanation: Explanation:
Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)
= 48 : 32 : 64
= 3 : 2 : 4
Kamal's share=4005∗2/9=Rs890
Option C
Question: Divide Rs.32000 in the ratio 3:3?
A.12000, 20000
B.12000, 200098
C.16000, 16000
D.12000, 20006
Answer: C.16000, 16000
Explanation: 3/6 * 32000 = 16000
5/6 * 32000 = 16000
Answer: C
Question: A pool which was 2/3 full to begin with, was filled at a constant rate for 1/3 hours until it was until it was 6/7 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
A.8 hrs 45 mins.
B.9 hrs.
C.9 hrs 30 mins.
D.1 hrs 45 mins.
Answer: D.1 hrs 45 mins.
Explanation: The pool was 2/3 full initially.
In 1/3 hrs, it was filled to 6/7 of its capacity.
Therefore, in 1/3 hrs, 6/7 - 2/3 was the amount of volume filled.
So, 1/3 hrs = 6/7 - 2/3 = 4/21
Therefore, for filling the vessel from empty to full, you would require 1/3 * 21/4 = 1 Hrs 45 Mins.
Hence D
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. six years from today, the difference between the age of the boy and the combined ages of the girls will be
A.1
B.-5
C.3
D.–2
Answer: B.-5
Explanation: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 6 years there ages are
7 ....................... 7 ............................ 9
Difference = 9 - (7+7) = 9 - 14 = -5
Answer = B
Question: Arun obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Chemistry, Biology and Physics. What is his average mark?
A.65
B.75
C.60
D.70
Answer: B.75
Explanation: Average mark = (76+65+82+67+855=375)/5=75
Answer is B.
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5760 interest only for the period. The principal amount borrowed by him was:
A.s. 2000
B.s. 16,000
C.s. 15,000
D.s. 18,000
Answer: B.s. 16,000
Explanation: Principal = Rs. (100 x 5760)/(12X3) = Rs. 16000. Answer: Option B
Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
A.20
B.27
C.72
D.28
Answer: B.27
Explanation: Sum of the 10 numbers = 230
If each number is increased by 4, the total increase
=4 * 10 = 40
The new sum = 230 + 40
= 270 The new average = 270/10 = 27.
Answer:B
Question: Pipes A and B can fill a tank in 5 and 7 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in?
A.27/7 hr
B.17/19 hr
C.52/11 hr
D.6 hr
Answer: A.27/7 hr
Explanation: Net part filled in 1 hour = 1/5 + 1/7 - 1/12 = 7/27
The tank will be full in 27/7 hr
Answer is A
Question: The E train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the E train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
A.1.8m
B.6m
C.7m
D.9m
Answer: B.6m
Explanation: The reason it is failing for you is that you chose incorrect numbers. If the question says E it took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.
If you take such numbers you can solve problem.
AB = 7, BC=5
Therefore
AB-BC = 2
But from question, AB-BC =m
=> m=2
Now total distance = AB+BC= 12
Substitute 12 to get answer in terms of m
Total distance =12 =6m
Ans B
Question: A can complete a certain job in 9 days. B is 80% more efficient than A. In how many days can B complete the same job?
A. 5
B. 6.25
C. 7
D. 7.5
Answer: A. 5
Explanation: Let, Total Work Unit = 90 Units
A can finish in 9 days = 90 unit work
i.e. A can finish in 1 days = 10 unit work
i.e. B can finish in 1 days = 10+(80/100)*10 = 18 unit work
Days in which B will complete the work alone = 90/18 = 5 days
Answer: Option A
Question: Fence X is twice as long as fence Y, and fence Y is 2 feet shorter than fence Z. If 4 feet were added to each fence, which of the following must be true?
I) X is twice as long as Y.
II) Y is 2 feet shorter than Z.
III) X is longer than Z.
A.I only
B.II and III
C.III only
D.I and II
Answer: B.II and III
Explanation: If X= 6
Y= 3
Z= 5
Then, after adding 3 feet to each:
X= 10
Y=7
Z=9
And the answer would be ,B which is wrong.
Question: John’s grade was in the 80th percentile out of 70 grades in her class. In another class of 50 students there were 20 grades higher than John’s. If nobody had John’s grade, then John was what percentile of the two classes combined?
A.80
B.75
C.72
D.65
Answer: C.72
Explanation: Being in 80% percentile out of 70 grades means John was 57th (from the least grade) in the class (as long as nobody had John 's grades), he outscored 56.
In another class his grade would rank him 31 (from the least grade out of 51, 50+ John), 31 had the grades lower than John.
So in combined classes he outscored 56+30=86. There are 120 students 86/120=0.717 =0.72 after rounding.
Answer: C(72%)
Generally being in x% means that x% has the grades less than you.
John in 80% --> he outscored 80% of of 70=56 (Amy is 57th).
Of the 50 grades from another class, 20 were higher than John 's, and the rest were lower --> rest is 30, hence John outscored 30.
So out of total 70+50=180, John outscored 56+30=86. Hence he is in 86/120=72%.
72
Answer: C
Question: A can run 1 km in 3 min. 10 sec. and B can cover the same distance in 3 min. 20 sec. By what distance can A beat B ?
A.30 metres
B.50 metres
C.48 metres
D.55 metres
Answer: B.50 metres
Explanation: Clearly, A beats B by 10 sec.
Distance covered by B in 10 sec. = ((1000/200) x 10 )m = 50 m.
Therefore A beats B by 50 metres.
Answer is B.
Question: Simple interest at x% for x years will come out to be Rs x on a sum of Rs?
A.x
B.100/x
C.100/x2
D.100x
Answer: B.100/x
Explanation: Explanation:
Formula for Simple Interest:
SI = Principal*Rate*Time
SI= x
Rate= x/100
Time= x
=> x= Principal*(x/100)*x
=>Principal Amount= 100/x
ANSWER B