mathewhe/aqua_rat huggingface dataset:
Question: The price of a certain house this year is $140,000, which is 25 percent greater than the cost of the house last year. What was the price of the house last year?
(A) $112,000
(B) $114,000
(C) $116,000
(D) $118,000
(E) $120,000
Rationale: The price of the house last year was $140,000/1.25=$112,000
The answer is A.
Answer: (A) $112,000
Question: The ratio between x and y is 8/3; x is multiplied by x and y is multiplied by y , what is the ratio between the new values of x and y?
(A) 8/3
(B) 3/8
(C) 1
(D) 64/9
(E) It Cannot Be Determined
Rationale: Ratio = 7k/9k = 7/9, 14/18, etc.
x is multiplied by x and y is multiplied by y --> (7k*7k)/(9k*9k) = 49k^2 / 81k^2 =49/81 =7/9
Answer: A
Answer: (A) 8/3
Question: A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the followings must be a prime number?
g(7) + 2; g(7) + 3; g(7) + 4; and g(7) + 5?
(A) 1
(B) 2
(C) 3
(D) 4
(E) none
Rationale: g(7) is the product of all integers from 1 to 7, so g(7) = 7!
Thus g(7) is a multiple of all the integers from 1 to 7.
Then g(7) is a multiple of 2, 3, 4, and 5.
2 divides g(7)+2
3 divides g(7)+3
4 divides g(7)+4
5 divides g(7)+5
The answer is E.
Answer: (E) none
Question: Three unbased coins are tossed. the probability of getting at least two head is ?
(A) 1/4
(B) 1/2
(C) 3/4
(D) 2/3
(E) 2/5
Rationale: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}
E be the event of getting at least two head is {THH,HTH,HHT,HHH}
P(E)=n(E)/n(S)=4/8=1/2
Answer(B)
Answer: (B) 1/2
Question: The distance light travels in one year is approximately 5,890,000,000,000 miles. The distance light travels in 100 years is
(A) A) 587 × 108 miles
(B) B) 587 × 1010 miles
(C) C) 587 × 10-10 miles
(D) D) 589 × 1012 miles
(E) E) 587 × 10-12 miles
Rationale: The distance of the light travels in 100 years is:
5,890,000,000,000 × 100 miles.
= 589,000,000,000,000 miles.
= 589 × 1012 miles.
The answer is (D)
Answer: (D) D) 589 × 1012 miles
Question: Adding 35% of x to x is equivalent to multiplying x by which of the following?
(A) 12.5
(B) 1.05
(C) 1.35
(D) 1.2
(E) 1.25
Rationale: 135x/100= 1.35*x
ANSWER:C
Answer: (C) 1.35
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
(A) Rs. 45
(B) Rs. 50
(C) Rs. 55
(D) Rs. 60
(E) None
Rationale: Solution: A : B : C = (10 * 7) : (12 * 5) : (15 * 3) = 70 : 60 : 45 = 14 : 12 : 9.
C's rent = Rs.(175 * 9/35) = Rs. 45.
Answer: Option A
Answer: (A) Rs. 45
Question: A company has two models of computers, model X and model Y. Operating at a constant rate, a model X computer can complete a certain task in 60 minutes and a model Y computer can complete the same task in 30 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model X computers were used?
(A) 18
(B) 16
(C) 15
(D) 17
(E) 20
Rationale: Let's say 1 work is processing 60 gb of data.
Model X : 1 gb per min
Model Y : 2 gb per min
Working together, 1 X and 1 Y = 3 gb per min
So, 20 times as many computers would work at 60 gb per min.
So no. of X =20
Answer is E
Answer: (E) 20
Question: A set M contains element all even number between 1 and 23 and all odd numbers 24 and 100. if all the elements of the set multiplied than how many trailing 0 , resulting number will contains?
(A) 10
(B) 12
(C) 9
(D) 8
(E) 7
Rationale: m={10,20 } &{25,35,45,55,65,75,85,95}
in set m number of 5 is 12.
ANSWER:B
Answer: (B) 12
Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 3 (B + G) is ?
(A) Equal to 3
(B) Less than 3
(C) More than 3
(D) Less than 1/3
(E) none of these
Rationale: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3
ANSWER:C
Answer: (C) More than 3
Question: Two trains 200m and 160m long run at the speed of 68kmph and 40kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
(A) 5.6sec
(B) 8.9sec
(C) 10.8sec
(D) 12 sec
(E) 15sec
Rationale: Relative speed = 68+40 = 108kmph * 5/18 = 30 m/s
Distance covered in crossing each other = 200+160 = 360m
Required time = 360*1/30 = 12 sec
Answer is D
Answer: (D) 12 sec
Question: Anne bought doughnuts for a class breakfast party. She bought 12 chocolate doughnuts, 12 coconut doughnuts, and 10 jam-filled doughnuts. How many doughnuts did Anne buy in all?
(A) 25
(B) 34
(C) 39
(D) 21
(E) 11
Rationale: Add the numbers of doughnuts.
12 + 12 + 10 =34.
Answer is B.
Answer: (B) 34
Question: A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job?
(A) 22
(B) 21
(C) 77
(D) 99
(E) 12
Rationale: WC = 1:2
2x + x = 1/14 => x = 1/42
2x = 1/21 => 21 days
Answer: B
Answer: (B) 21
Question: The mass of 1 cubic meter of a substance is 400 kilograms under certain conditions. What is the volume, in cubic centimeters, of 1 gram of this substance under these conditions? (1 kilogram = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
(A) 0.8
(B) 1.25
(C) 8.0
(D) 2.5
(E) 80.0
Rationale: Density is mass divided by volume. So density of the given substance will be mass/volume=400kg/1m^3=400 kg/m^3 or 1g/2.5cm^3=0.4 g/cm^3.
Next, ask yourself if 400,000 g is equivalent to 1,000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters? --> 1 g - 1,000,000/400,000 = 10/4 = 2.5 cubic centimeters.
Answer is D
Answer: (D) 2.5
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B =2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
(A) 20.23
(B) 18
(C) 30.93
(D) 20.93
(E) 10.93
Rationale: A:B = 2:3
B:C = 2:5
A:B:C =4:6:15
6/25 * 75 = 18
ANSWER:B
Answer: (B) 18
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.32000?
(A) 81000
(B) 33888
(C) 77678
(D) 200988
(E) 40500
Rationale: 32000* 9/8 * 9/8
= 40500
Answer: E
Answer: (E) 40500
Question: When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country?
(A) 166 2/9
(B) 166 2/5
(C) 166 2/8
(D) 166 2/3
(E) 166 2/1
Rationale: 5% - 2% = 3%
3% ---- 5
100% ---- ?
=> 166 2/3
Answer:D
Answer: (D) 166 2/3
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 60 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 15 min
(B) 15 1/7 min
(C) 17 1/7 min
(D) 7 1/7 min
(E) 7 2/7 min
Rationale: 1/20 + 1/30 - 1/60 = 4/60
60/4 = 15
ANSWER:A
Answer: (A) 15 min
Question: A goods train runs at a speed of 72 kmph and crosses a 260 m long platform in 26 seconds.What is the length of the goods train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 270 m
(E) 250 m
Rationale: s=260+x/t
72*5/18=260+x/26
x=260
ANSWER:C
Answer: (C) 260 m
Question: Along a yard 225 metres long, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Explanation:
26 trees have 25 gaps between them,
Required distance (225/25) = 10
Option B
Answer: (B) 9
Question: Three printing presses, W, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take W, working alone at its constant rate, to do the same job?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 20
Rationale: =1/4-1/5=1/20
W can do 1/20 job in 1 hour
W can do the whole job in 20 hours=E
Answer: (E) 20
Question: An urn contains 5 red, 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that the drawn ball are 2 blue and 1 red?
(A) 25/323
(B) 21/969
(C) 28/989
(D) 74/879
(E) 23/589
Rationale: Sample space = no. of ways 3 balls were drawn from urn = 19C3 = 969
No. ways 2 blue balls and 1 red were drawn from bag = 6C2 * 5C1 = 75
Probability = 75 / 969 =25/323
Ans - A
Answer: (A) 25/323
Question: If the SI on a certain sum of money is 4/25 of the sum and the rate per cent equals the number yrs, then the rate of interest/annum is?
(A) 4%
(B) 55
(C) 6%
(D) 7%
(E) 9%
Rationale: Sol Let the prmcipal be Rs. x
Then the simple interest (1)
Let the me ofinterestp 3 be 1%,
than tune m : ryears
max! max
pm
‘X:5
4%
A
Answer: (A) 4%
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 228
(B) 277
(C) 500
(D) 288
(E) 212
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters.Answer:C
Answer: (C) 500
Question: Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
(A) 864
(B) 863
(C) 865
(D) 1728
(E) 890
Rationale: Explanation :
The required number of ways :-
=>3C2×4!×4!.
=>1728.
Answer : D
Answer: (D) 1728
Question: The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 41 on the fourth day, his average earning for the whole week is ?
(A) Rs . 18.95
(B) Rs 16
(C) Rs. 17
(D) Rs. 25.71
(E) None of these
Rationale: Answer
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 -41
= Rs. 119
âˆ´ Average earning = 119 / 7
= Rs. 17
Correct Option: C
Answer: (C) Rs. 17
Question: FOG + FOG + FOG + FOG = 1444.
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) 10
(E) 15
Rationale: given,FOG + FOG + FOG + FOG = 1444
4(FOG)=1444
=>FOG=361
Face value of F is:3
Face value of O is:6
Face value of G is:1
so F+O+G=3+6+4=10
ANSWER:D
Answer: (D) 10
Question: A fruit wholesale dealer has been paid $329,864 in his savings account. What is the least amount of money (in whole number of dollars) that he must add to his account if if he wants to be sure that all 9 of his salesmen have paid evenly?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $6
Rationale: To find the least amount the fruit wholesale dealer should add to his account to ensure all 9 of his salemen have paid evenly,
he needs to make the total divisible by 9
Simply add the individual digits of the total = 3+2+9+8+6+4 = 32
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Answer: (D) $4
Question: If m,n,o,p are four consecutive even numbers, their average is
(A) (m + 3)
(B) 5(m+4)
(C) 5(m+n+o+p)
(D) mnop
(E) None of these
Rationale: Explanation :
Clearly,n=m+2,o=m+4,p=m+6.
Average (m + (m + 2) + (m + 4) + (m + 6)) / 4
= (4m + 12) / 4
= (m + 3)
Answer : A
Answer: (A) (m + 3)
Question: A shopkeeper sold an article at $100 with 45% profit. Then find its cost price?
(A) $120
(B) $100
(C) $91
(D) $72
(E) $69
Rationale: cost price = selling price *100/(100+profit)
C.P. = 100*100/145 = $69(approximately)
Answer is E
Answer: (E) $69
Question: Six lights begin to flash together at 12:00 noon and flash respectively at intervals of 3, 4, 5, 6, 7, and 8 seconds. Not including the flash at 12:00 noon, how many more times will all six lights flash together before 1:00 pm (i.e. one hour later)?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: The least common multiple is 2*2*2*3*5*7=840.
3600 seconds / 840 = 4 + remainder.
The answer is A.
Answer: (A) 4
Question: A caterer ordered 125 ice-cream bars and 125 sundaes. If the total price was $225.00 and the price of each ice-cream bar was $0.60, what was the price of each sundae?
(A) $0.60
(B) $0.80
(C) $1.00
(D) $1.20
(E) $1.60
Rationale: Let price of a sundae = S
Price of ice cream bar = .6 $
125 * .6 + 125*S = 225
=> 125*S = 150
=> S = 1.2
Answer D
Answer: (D) $1.20
Question: If a can do a work in 10 days and a and b can do a same piece of job in 5 days. IN how days can do a work b alone?
(A) 10
(B) 20
(C) 5
(D) 15
(E) 9
Rationale: a's one day work=1/10
a+b=1/5(one day work)
b=(1/5)-a=(1/5)-(1/10)
=1/10(one day work)
b can done a work in 10 days.
Answer option A
Answer: (A) 10
Question: How many terms are in the G.P. 3, 6, 12, 24, ......., 384 ,768,1536
(A) 8
(B) 9
(C) 67
(D) 5
(E) 10
Rationale: Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 384 => a * r^(n-1) = 1536
=> 3 * 2^(n-1) = 1536 => 2^(n-1) = 512 = 2^(9)
=> n-1 = 9 => n = 10
Answer: E
Answer: (E) 10
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 2 buckles is how many times that of 4 buckles and 6 buttons?
(A) 7/15.
(B) 4/9.
(C) 6/11.
(D) 1/2.
(E) 8/15.
Rationale: 2buttons + 2buckles = 1/3(11buckles + 3buttons)
6buttons + 6buckles = 11buckles + 3buttons
3buttons = 5buckles
Weight of 3buttons and 2buckles = 5buckles + 2buckles = 7buckles
Weight of 6buttons and 5buckles = 10buckles + 4buckles = 14buckles
(3buttons and 2buckles) = x * (6buttons and 5buckles)
7 = x*14
x = 7/14=1/2
Answer: D
Answer: (D) 1/2.
Question: A 4-letter code word consists of letters L, M, AND N. If the code includes all the three letters, how many such codes are possible?
(A) 72
(B) 36
(C) 24
(D) 44
(E) 22
Rationale: Note that the correct answer to this question is 36, not 72.
L-LMN can be arranged in 4!/2!=12 ways;
M-LMN can be arranged in 4!/2!=12 ways;
N-LMN can be arranged in 4!/2!=12 ways;
Total: 12+12+12=36.
Answer: B
Answer: (B) 36
Question: At a certain organisation, the number of male members went up by 14% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000?
(A) 1:2
(B) 1:3
(C) 2:3
(D) 3:2
(E) 4:7
Rationale: men increase by 14% ==> 1.14M = males in 2001
women decrease by 6% ==> 0.94F = women in 2001
total employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001
Obviously
(males in 2001) + (females in 2001) = total number of employees in 2001
1.14M + 0.94F = 1.012*(M + F)
1.14M + 0.94F = 1.012M + 1.012F
1.14M - 1.012M = 1.012F - 0.94F
0.128M = 0.072F
M/F = (0.072)/(0.128) = 72/128 = 4/7
Answer =(E)
Answer: (E) 4:7
Question: A candidate got 35% of the votes and lost to the rival by 1350 votes. How many votes were cast?
(A) 4000
(B) 4500
(C) 5000
(D) 5500
(E) 6000
Rationale: 35%-----------L
65%-----------W
------------------
30% = 1350
10% = 450
100% of the votes = 4500
Answer: B
Answer: (B) 4500
Question: A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?
(A) 1200
(B) 1300
(C) 1500
(D) 1400
(E) 1700
Rationale: Assume that the total profit is x
Since 5% goes for charity, 95% of x will be divided between A and B in the ratio 3:2
Therefore, A's profit =(95x/100)×(3/5)
Given that A's share is Rs. 855. Therefore,
(95x/100)×(3/5)=855
⇒95x/100=855×5/3=285×5=1425
⇒x=1425×100/95
=285×100/19=1500
Answer is C.
Hence the total profit = 1500
Answer: (C) 1500
Question: How many positive integers less than 100 have a remainder of 2 when divided by 13?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 6
Rationale: take the multiples of 13 and add 2
0X13+2=2 ....13X7+2=93
there are 14 numbers
answer C
Answer: (C) 8
Question: When the positive integer a is divided by 11, the quotient is b and the remainder 3. When a is divided by 19, the remainder is also 3. What is the remainder when b is divided by 19?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: Any Number which when divided by divisor d1,d2, etc. leaving same remainderrtakes the form ofK+r
where k = LCM (d1,d2)
In this case the divisors are 1119 and remainder is 3.
so LCM (11,19) = 209
So N= 209+3 = 212
Also a=d1q+3 ; which means d1q=209d1=11 therefore q=19
And ( b divided by 19)19/19 leaves remainder 0.
Answer is E
Answer: (E) 0
Question: There are 6periods in each working day of a school. In how many ways can 1 arrange 5subjects such that each subject is allowed at least 1period?
(A) 1200
(B) 1800
(C) 2000
(D) 2500
(E) 2600
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Remaining 1 period can be arranged in 5P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements = (6P5 x 5P1)/2! = 1800
Alternatively this can be derived using the following approach.
5 subjects can be selected in 5C5 ways.
Remaining 1 subject can be selected in 5C1 ways.
These 6 subjects can be arranged themselves in 6! ways.
Since two subjects are same, we need to divide by 2!
Total number of arrangements = (5C5 × 5C1 × 6!)/2! = 1800
B
Answer: (B) 1800
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:
(A) 14 hrs
(B) 15 hrs
(C) 10 hrs
(D) 20 hrs
(E) 25 hrs
Rationale: work done in 1 hr = 1/2-3/7 = 1/14
==>14 hrs
ANSWER A
Answer: (A) 14 hrs
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 50
(B) 54
(C) 52
(D) 56
(E) 58
Rationale: Explanation:
speed= Distance/ Time
S = 240/16 * 18/5 = 54 kmph
Answer:B
Answer: (B) 54
Question: In a certain accounting class of 100 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 60%, and the students on the make-up date had an average score of 80%, what was the average score for the entire class?
(A) 64%
(B) 66%
(C) 68%
(D) 70%
(E) 72%
Rationale: 70% of the class scored 60% and 30% of the class scored 80%.
The difference between 60% and 80% is 20%.
The average will be 60% + 0.3(20%) = 66%.
The answer is B.
Answer: (B) 66%
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job.How long should it take both A and B, working together but independently, to do the same job?
(A) 40/9 days
(B) 9 days
(C) 40 days
(D) 94 days
(E) 7 days
Rationale: A’s 1 hour's work = 1/8
B's 1 hour's work = 1/10
(A + B)'s 1 hour's work = (1/8) +(1/10)=9/40
Both A and B will finish the work in 40/9 days.
Ans: A
Answer: (A) 40/9 days
Question: A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?
(A) 316/439
(B) 316/438
(C) 316/435
(D) 316/299
(E) 316/199
Rationale: Let A be the event of getting two oranges and
B be the event of getting two non-defective fruits.
and be the event of getting two non-defective oranges
Answer: C) 316/435
Answer: (C) 316/435
Question: Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 8
Rationale: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
B
Answer: (B) 3
Question: The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 50 more than the number who did not, and if receipts for registration and lunch totaled $82,900, how many people paid just for registration at the meeting?
(A) 700
(B) 650
(C) 1,300
(D) 1,500
(E) 1,800
Rationale: Hope this might be useful to you.
Let the number of people who have opted only to register = x
Now since the registration cost is 50$ per person, the total amount sums to = 50x $
As per the information given in the question, the number of registrants who paid for lunch was 50 more than the number who did not. That means, total number of people who registered and paid for lunch = 50 + x.
For the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $.
Total amount in this case sums to = 72(50 + x) = 3600 + 72x
Now, total amount received was 82900.
Thus, from the above data,
50x + 3600 + 72x = 82900
122x = 82900 - 3600
122x = 79300
x = 650
Hence the correct Ans is B
Answer: (B) 650
Question: A bullock cart has to cover a distance of 80km in 10hrs. If it covers half of the journey in 3/5th time. what should be its speed to cover the remaining distance in the time left.
(A) 10 kmph
(B) 20 kmph
(C) 30 kmph
(D) 40 kmph
(E) 50 kmph
Rationale: A
10 kmph
Time left = 10 - 3/5*10
= 4 hr 10 km/h
speed =40 km /4 hr
=10 kmph
Answer: (A) 10 kmph
Question: If 30 oxen can plough 1/7th of a field in 2 days, how many days 18 oxen will take to do the remaining work?
(A) 30 days
(B) 20 days
(C) 15 days
(D) 18 days
(E) 21 days
Rationale: Solution: We will use work equivalence method,
30/18 = (1/7)/(6/7)*x/2;
5/3 = (1/6)*x/2;
Or, x = 60/3 = 20 days.
Answer: Option B
Answer: (B) 20 days
Question: A shopkeeper sells 500 metres of cloth for Rs. 15000 at a loss of Rs.10 per metre. Find his cost price for one metre of cloth?
(A) s.40
(B) s.12
(C) s.96
(D) s.50
(E) s.13
Rationale: SP per metre = 15000/500
= Rs. 30 Loss per metre
= Rs. 10 CP per metre = 30 + 10
= Rs.40
Answer: A
Answer: (A) s.40
Question: 15 percent of new students select a science major, 10 percent select an arts major, and 35 percent select an engineering major, what fraction of students remain undecided?
(A) 4/5
(B) 3/5
(C) 3/10
(D) 2/5
(E) 1/10
Rationale: 100%-(15%+10%+35%)=60% remains for other allocations --> 40% = 40/100 = 2/5.
Answer: D.
Answer: (D) 2/5
Question: The present ages of three persons in proportions 5 : 6 : 4. Five years ago, the sum of their ages was 60. Find their present ages (in years).
(A) 8, 20, 28
(B) 16, 28, 36
(C) 25,30,20
(D) 18, 24, 32
(E) None of these
Rationale: Explanation:
Let their present ages be 5x, 6x and 4x years respectively.
Then, (5x - 5) + (6x - 5) + (4x - 5) = 60
15x-15 = 60
x = 5
Their present ages are 5x = 25 years, 6x = 30 years and 4x = 20 years respectively.
Answer: C
Answer: (C) 25,30,20
Question: The number of new words that can be formed by rearranging the letters of the word 'LIVE' is?
(A) 25
(B) 27
(C) 19
(D) 23
(E) 24
Rationale: Number of words which can be formed
= 4! - 1 = 24- 1
= 23.
Answer:D
Answer: (D) 23
Question: Number of ways in which the letters of word AMBI can be arranged with vowels in alphabetical order, is
(A) 360
(B) 240
(C) 12
(D) 480
(E) None of these
Rationale: Solution
Order of vowels of fixed
âˆ´ required number of ways are 4!/2!.
Answer C
Answer: (C) 12
Question: The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 420 kms in 4 hours, then the speed of the first train is:
(A) 89.25 km/hr.
(B) 37.25 km/hr.
(C) 90.25 km/hr.
(D) 94.25 km/hr.
(E) 91.875 km/hr.
Rationale: Let the speed of two bullet trains be 7x and 8x km/hr.
Then, 8x = (420/4) = 105
x = (105/8) = 13.125
Hence, speed of first bullet train = (7 x 13.125) km/hr = 91.875 km/hr.
E
Answer: (E) 91.875 km/hr.
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
(A) 3:4
(B) 4:5
(C) 6:3
(D) 4:4
(E) 3:7
Rationale: A
3:4
Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 --> 1/x + 4/y = 1/15 ------ (i)
Also, 200/x + 400/y = 25/3 --> 1/x + 2/y = 1/24 ----(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
--> Ratio of speeds = 60 : 80 = 3 : 4.
Answer: (A) 3:4