divelab/Sys2Bench huggingface dataset:
Question: I flew my tiny seaplane to visit my mother. On the flight up, I flew at 110 mph. On the way home, I flew 90 mph. What was my average speed for the trip?
Options:
A)198 mph
B)110 mph
C)88 mph
D)100 mph
E)99 mph
Rationale: (110 mph +90 mph)/2= 100 mph
Correct answer is: D
Answer: D
Question: Of the three-digit integers greater than 200, how many have two digits that are equal to each other and the remaining digit different from the other two?
Options:
A) 90
B) 82
C) 80
D) 45
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 > 200.
Answer:(E)
Answer: E
Question: The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic i
Options:
A)66
B)20
C)12
D)21
E)71
Rationale: Explanation:
Let the initial number of persons be x. Then,
16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x = 10 <=> x = 20.
Answer: B
Answer: B
Question: If 4/(a + 5) = 7/(a - 4), then a = ?
Options:
A)-15
B)-19
C)-17
D)-18
E)-13
Rationale: Multiply all terms of the given equation by (a + 5)(a - 4), simplify and solve
(a + 5)(a - 4)[ 4/(a + 5) ] = (a + 5)(a - 4) [ 7/(a - 4) ]
4 (a - 4) =7 (a + 5)
a = -17
correct answer C
Answer: C
Question: If the product of two numbers is 45276 and their H.C.F. is 22, find their L.C.M.
Options:
A)2574
B)2500
C)2100
D)2058
E)None of these
Rationale: Explanation:
HCF * LCM = 45276, because we know
Product of two numbers = Product of HCF and LCM
LCM = 45276/22= 2058
Option D
Answer: D
Question: Amit started walking positioning his back towards the sun. After some time, he turned left, then turned right and towards the left again. In which direction is he going now?
Options:
A)North or South
B)East or West
C)North or West
D)South or West
E)none
Rationale: North or south
ANSWER:A
Answer: A
Question: Twenty participants are participating in a competition. In how many ways can the first three prizes be won?
Options:
A)920
B)680
C)820
D)720
E)6840
Rationale: Out of 20 participants, the first three prizes can be won in,
20P3 = 20! / (20 - 3)!
= 20 x 19 x18
= 6840 ways
ANSWER:E
Answer: E
Question: If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?
Options:
A)11
B)12
C)13
D)48
E)51
Rationale: Number of factors of N=a^x∗b^y where 'a' and 'b' are prime factors of N is
(X+1) (y+1)
So 4 (y+1)=52
y=12
ANSWER:B
Answer: B
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent?
Options:
A)200
B)278
C)100
D)202
E)270
Rationale: Profit on first article = 10% of 1000 = 100.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: C
Answer: C
Question: The speed of three cars in the ratio 5 : 4 : 6. The ratio between the time taken by them to travel the same distance is
Options:
A)5 : 4 : 6
B)6 : 4 : 5
C)12 : 15 : 10
D)10 : 12 : 15
E)None
Rationale: Sol.
Ratio of time taken = 1 / 5 : 1/4 : 1/6 = 12 : 15 : 10.
Answer C
Answer: C
Question: A and B starts a business with Rs.8000 each, and after 9 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
Options:
A)4:3
B)18:5
C)14:10
D)18:14
E)14:11
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 9 months and then withdraws Rs.4000. So, the investment of B for remaining 9 months is Rs.4000 only.
A : B
8000*18 : (8000*9) + (4000*9)
14400 : 108000
A:B = 4:3
Answer: A
Answer: A
Question: The first ticket is purchased at $2,40 and then the following purchases of ten tickets costs $2,20/ticket. What is the total number of tickets purchased if $90,40 is paid?
Options:
A)38
B)39
C)40
D)41
E)42
Rationale: a is the number of ten packs of tickets.
90,40 = 2,40 + 10 * 2,20 *a
a = 4
The total number of tickets --> 4*10+1 = 41
Answer: D
Answer: D
Question: In a certain population, there are 2 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is
Options:
A) 1 to 2
B) 1 to 3
C) 1 to 4
D) 2 to 3
E) 3 to 4
Rationale: Consider the ratio of the under population of 21 to over the 21 as 2:1
therefore 2x:1X
Now the ratio of the under to the whole population becomes 2x/2x+1x
= 2/3
Answer is D
Answer: D
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 5/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
Options:
A)7/16
B)7/15
C)10/21
D)17/35
E)5/14
Rationale: Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;
Let the price of small cup be $6, then the price of larges cup would be 5/6*6=$5;
Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$5=$20;
Fraction of total revenue from large cups: 20/(36+20)=5/14.
Answer: E
Answer: E
Question: Set A of 8 positive integers may have the same element and have 39. And set B of 8 positive integers must have different elements and have 39. When m and n are the greatest possible differences between 39 and other elements’ sums in set A and set B, respectively, m-n=?
Options:
A)20
B)23
C)21
D)25
E)26
Rationale: This is maximum-minimum. Hence, 39-(1+1+1+1+1+1+1)=32 and 39-(1+2+3+4+5+6+7)=11. So, 32-11=21. The correct answer is C.
Answer: C
Question: The line P represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1
Options:
A)y = 2x^2+5x+1
B)y = x^2+5x+2
C)y = 3x^2+5x+2
D)y = 3x^2+7x+2
E)y = x^2+7x+1
Rationale: concept of slope for linesparabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.
The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.
We have a similar form as x^2 = 4ay.
here the vertex is origin.
So if we have same values of x and y but constant term changes then we will have parallel parabolas.
This is same as for straight line P which are parallel for different values of constant term c
ax + by +c1 = 0 and ax +by+ c2 =0
We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.C
Answer: C
Question: Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 20 as remainder
Options:
A)1235
B)1456
C)1634
D)1678
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 20
5x = 1345
x = 269
Large number = 269+1365 = 1634
C
Answer: C
Question: What quantity of water should taken out to concentrate 21 liters of 40% acidic liquid to 60% acidic liquid?
Options:
A)5liters
B)10liters
C)7liters
D)8liters
E)6liters
Rationale: Required answer is = 21(60-40)/60 = 7 liters
Answer is C
Answer: C
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 30% but the selling price
remains constant, approximately what percentage of the selling price is the profit
Options:
A)69%
B)89%
C)99%
D)100%
E)None of above
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 130% of Rs. 100 = Rs. 130
New S.P. = Rs. 420.
Profit = Rs. (420 - 130) = Rs. 290
Required percentage = (290/420) * 100
= 69%(approx)
Answer: A
Answer: A
Question: There is 60% increase in an amount in 6yrs at SI. What will be the CI of Rs. 12,000 after 3 years at the same rate?
Options:
A)2354
B)2450
C)2540
D)2650
E)3972
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
C.I.
= Rs. 12000 x 1 + 10 3 - 1
100
= Rs. 12000 x 331
1000
= 3972.
E
Answer: E
Question: A wolf eats 6 Kg of meat in 2 days. A baby tiger eats 3 Kg of meat in 4 days. How much meat can the two combined eat in three days?
Options:
A)11.25
B)9.25
C)8.5
D)7.5
E)6.25
Rationale: 3/2*6+3/4*3=11.25kg
A
Answer: A
Question: A man goes into a barbershop and gets a $15 haircut. He pays the barber with a $20 bill, but the barber doesn't have change because it is an especially slow day. The barber goes to the flower shop next to his own and trades the $20 bill for a $10 dollar bill and two $5 bills. Then he gives the man his $5 in change.
Later the lady from the flower shop confronts the barber and tells him that the $20 bill he gave her was counterfeit. The barber agrees and he gives the lady a different $20 bill.
Later that day he tries to figure out how much money he lost. What did he lose?
Options:
A)$5
B)$10
C)$12
D)$15
E)$20
Rationale: He lost $5. The lady from the flower shop gave him $20 in change, but eventually got $20 back. She broke even. The man who got the haircut gave the barber nothing (except counterfeit money) but got $5 back from the barber. So the barber lost only $5, and gave a free haircut.
Answer: A
Question: Mr. loyd wants to fence his Square shaped land of 60Sqft each side.If a pole is laid every 12ft how many poles do he need?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: If each side is 120 feet..then total perimeter is 60*4=240
poles every 12 feet hence no of poles= 240/12=20
ANSWER:A
Answer: A
Question: A train crosses a platform 100 m long in 60 seconds at a speed of 45 kmph.The time taken by the train to cross an electric pole is
Options:
A)8 sec
B)52 sec
C)1 minute
D)2 minute
E)data inadequate
Rationale: let the length of the train be x m.
and that of platform is 100m.
:., Total distance covered = (x+100)m
Speed of the train= 45 km/hr. = 45*5/18 m/s = 12.5 m/s
Since it crosses the platform in 60 sec.
So, (x+100)/12.5=60
or, x=60*12.5-100=650m
It will cross an electric pole in 650m/12.5m/s=52sec.
ANSWER:B
Answer: B
Question: It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 140 pages?
Options:
A)12
B)18
C)20
D)42
E)30
Rationale: If it takes 4 more minutes for A to print 40 pages than it takes B,
it takes 5 more minutes for A to print 50 pages than it takes B.
Thus if b is the number of minutes than B takes to print 50 pages,
we can write:
1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)
6(2b+5)=b(b+5)
b^2-7b-30=0
(b-10)(b+3)=0
b=10
Thus it takes A 15 minutes to print 50 pages and 15*140/50=42 minutes to print 140 pages (ANSWER D)
Answer: D
Question: A cricketer scored 142 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
Options:
A)57.75%
B)54.54 %
C)63%
D)70%
E)None of these
Rationale: Explanation :
Number of runs made by running = 142 - (12 x 4 + 2 x 6)
= 142 - (60)
= 82
Now, we need to calculate 82 is what percent of 142.
=> 82/142 * 100 = 57.75 %
Answer : A
Answer: A
Question: The average earning of amechanic for the first 4days of a week is Rs.25 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
Options:
A)s. 10
B)s. 24
C)s. 30
D)s. 40
E)s. 50
Rationale: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x 25+ 4 x 22 -20
= Rs. 168
âˆ´ Average earning = 168/ 7
= Rs. 24
B
Answer: B
Question: A man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 2km on foot. His total journey is
Options:
A)16km
B)10km
C)12km
D)24km
E)25km
Rationale: Explanation:
Let the journey be x km
Then, 1x/2 + 1x/3 +2 =x
5x +12 =6x
X = 12km
Answer: Option C
Answer: C
Question: An electric wire runs for 1 km b/w some no: of poles. If one pole is removed the distance b/w each pole increases by 1 2/6 (mixed fraction). How many poles were there initially?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: let there be x no. of poles
distance b/w them= 1/(x-1)
now when one pole is removed
distance bw each pole=1/(x-2)
now according to the question
1/(x-2) =8/6 (1/x-1)
on solving you will get x=5
ANSWER:B
Answer: B
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between 6* + 2 and 6* + 6, inclusive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes in this range.
Answer: A.
Answer: A
Question: A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
Options:
A)102
B)60
C)75
D)90
E)95
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 544
16x = 544
x = 34.
Hence, total number of notes = 3x = 102
Answer: Option A
Answer: A
Question: Two numbers have a H.C.F of 9 and a product of two numbers is 1800. Find the L.C.M of the two numbers?
Options:
A)200
B)150
C)160
D)170
E)180
Rationale: L.C.M of two numbers is given by
(Product of the two numbers) / (H.C.F of the two numbers) = 1800/9 = 200.
ANSWER:A
Answer: A
Question: eight books consisting of 5 financial management, 2 marketing management and Since the denominator will be 11! . And there is no way to divide 11 from numerator and denominator. Use a multiple of 11 in the denominator only answer 1 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.
Options:
A)1/1155
B)1/5040
C)1/256
D)1/2255
E)1/1455
Rationale: Since the denominator will be 8! . And there is no way to divide8 from numerator and denominator. Use a multiple of 8in the denominator only answer
C
Answer: C
Question: The cost of 3 kg of sugar is $ 60. What will the cost of 8 kg of sugar be?
Options:
A)20
B)40
C)80
D)160
E)180
Rationale: This is a situation of direct variation, now we solve using unitary method.
Cost of 3 kg of sugar = $ 60
Cost of 1 kg of sugar = $ 60/3 = $ 20
Cost of 8 kg of sugar = $ 20 × 8
Therefore, cost of 8 kg of sugar = $ 160
ANSWER -D
Answer: D
Question: Nancy works 4 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?
Options:
A)a) 3y(7x+2xy)
B)b) 3x+12y
C)c) 3xy(7x+2)
D)d) 3x(2y+7)
E)e) 2x(3y+4)
Rationale: Payment of a week for 3 days a week = $4x
Payment of 4 weeks for 3 days a week = $4x*4 = $16x
Payment of a week for y days overtime a week = $4x+$2xy
Payment of 3 weeks for y days overtime a week = ($4x+$2xy)*3
Total Earnings = $16x + ($4x+$2xy)*3 = 28x+6xy =2x(3y+14)
Answer: option E
Answer: E
Question: If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:
Options:
A)2
B)4
C)6
D)3
E)8
Rationale: D
3
Given number = 97215x6
(6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.
x = 3
Answer: D
Question: If y = ||x – 3| – 2|, for how many values of x is y = 5?
Options:
A)2
B)1
C)3
D)4
E)5
Rationale: y = ||x – 3| – 2| can be 4 only and only when X-3= +/-7. so there are 2 values of X
Answer : A
Answer: A
Question: Sid left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?
Options:
A)40
B)200
C)266
D)267
E)600
Rationale: In order not to lose money because of the change Sid's total commission must beat least$75,000-$45,000=$30,000, so total sales must beat least$30,000/0.15=$200,000. Which means that he must makeat least$200,000/750=800/3=266.6 sales, so 267 sales.
Answer: D.
Answer: D
Question: An error 6% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
Options:
A)14.05%
B)14.02%
C)14%
D)13%
E)12.36%
Rationale: Percentage error in calculated area
=(6+6+(6Ã—6)/100)%
=12.36%
ANSWER:E
Answer: E
Question: A group of men decided to do a work in 50days, but 10 of them became absent. If the rest of the group did the work in 60days, Find the original number of men?
Options:
A)60
B)50
C)40
D)100
E)25
Rationale: Original number of men = 10*60 / (60-50) = 60
Answer is A
Answer: A
Question: What is the total number of ways in which Dishu can distribute 9 distinct gifts among his 8 distinct girlfriends such that each of them gets at least one gift?
Options:
A)72 * 8!
B)144 * 8!
C)36 * 8!
D)9!
E)None of these
Rationale: Solution:
As every girl friend should get one gift.
The number of ways 8 distinct gifts can be selected is: 9C8 = 9 ways.
The number of ways each GF gets one gift each out of these 8 selected gifts 8!
Total number of ways 8 gifts can be distributed is 9 *8!.
Now the last one gift can be given to any of the 8 GF hence, the total number of ways of distributing =(9 *8! *82)= 36 * 8! ways.
Answer: Option C
Answer: C
Question: The area of a rectangle is 63 sq m. The width is two meters shorter than the length. What is the width?
Options:
A)9
B)7
C)-9
D)11
E)6
Rationale: a = l x w
w = l - 2
l = w + 2
a = (w + 2 ) x w
a = w^2 + 2 x w
63 = w^2 + 2w
0 = w^2 + 2w - 63
0 = (w + 9)(w - 7)
w = -9 and w = 7, width cannot be negative so w = 7
Answer is B
Answer: B
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 30 ps per meter is?
Options:
A)s.122
B)s.105
C)s.125
D)s.120
E)s.121
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 30) = 210 m
210 * 1/2 = Rs.105
Answer:B
Answer: B
Question: In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
Options:
A)8 1/3
B)8 1/9
C)8 1/6
D)8 1/2
E)8 1/1
Rationale: (4000*3*R)/100 = (5000*5*4)/100
R = 8 1/3
Answer: A
Answer: A
Question: In one hour a boat goes 11 km long the stream and 5 km against the stream.The speed of the boat in still water is?
Options:
A)7
B)8
C)6
D)5
E)1
Rationale: Speed in still water A = ½ ( 11+5) km/hr A= 8 kmph
Answer: A
Answer: A
Question: what is the value of y if the greatest common divisor of (y-4)!,(y+1)!, and (y+2)! is 720.
Options:
A)12
B)10
C)9
D)7
E)8
Rationale: GCD of (y-4)!,(y+1)!, and (y+2)! is 720. Find y.
Best way to find n is substitute each of the answer and find out the correct one.
Only option B gave the correct answer.
Option B: 10 and find GCD or 6!, 11! and 12!. 6! itself is 720 and 6! which is contained in the other two factorials. This satisfies the condition, hence answer is 10.
Answer is B.
Answer: B
Question: The monthly rent of a shop of dimension 18feet × 22feet is Rs.2244. What is the annual rent per square foot of the shop? (a) Rs. 5(2/3)
Options:
A)43
B)56
C)68
D)87
E)92
Rationale: Sol. Monthly rent per square feet = 2244/(18*22)
& Annual rent per square feet
=12*(2244/(18*22))=68
C
Answer: C
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
Options:
A)202
B)200
C)209
D)207
E)201
Rationale: The number of ways to select two men and three women = ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer:B
Answer: B
Question: What will be the fraction of 50%
Options:
A)1/4
B)1/2
C)1/10
D)1/11
E)None of above
Rationale: Explanation:
It will 50*1/100 = 1/2
Option B
Answer: B
Question: The average of six integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 65, what is the least possible value of one of the other two integers?
Options:
A)45
B)62
C)75
D)83
E)90
Rationale: When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 63
So, the sum of ALL 5 integers = (63)(6) =378
The average of three of the integers is 65
So, the sum of the 3 integers = (65)(3) =195
So, the sum of the 2 REMAINING integers =378-195=183
If the sum of the 2 REMAINING integers =183, and we want to minimize one value, we must MAXIMIZE the other value.
100 is the maximum value so let 1 integer = 100, which means the other must equal 83
Answer: D
Answer: D
Question: Pipe A can fill a tank in 3 hours. Due to a leak at the bottom, it takes 6 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)67
B)88
C)4.5
D)26
E)12
Rationale: Let the leak can empty the full tank in x hours 1/3 - 1/x = 1/6
=> 1/x = 1/2 - 1/6 = 1/4.5
=> x = 4.5 Answer:C
Answer: C
Question: Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?
Options:
A)8 1/9
B)8 1/0
C)8 1/4
D)8 1/3
E)8 1/1
Rationale: 3/12 + (3 + x)/15 = 1
x = 8 1/4
Answer: C
Answer: C
Question: If mn ≠ 0 and 25 percent of n equals 37 1/2 percent of m, what is the value of 12n/m?
Options:
A)18
B)323323
C)8
D)3
E)98
Rationale: Given : 25 percent of n equals 37(1/2) percent of m => (25/100)*n = (75/200)*m => 2n = 3m.
12n/m = 6*2n/m = 6*3m/m = 18. Hence A.
Answer: A
Question: In a group of 3 boys and 7 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?
Options:
A)145
B)175
C)205
D)235
E)265
Rationale: Number of ways to select four children is 10C4 = 210
Number of ways to choose only girls is 7C4 = 35
Number of ways that at least one boy is selected is 210 - 35 = 175
The answer is B.
Answer: B
Question: what is the compound interest on rs:30,000 for 4 months at the rate of 5% per annum
Options:
A)501.13
B)502.13
C)503.13
D)504.13
E)505.13
Rationale: it is monthly compound
rate=5/12% per month
30000*(1+5/1200)^4-30000=503.13
ANSWER:C
Answer: C