divelab/Sys2Bench huggingface dataset:
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 17. What could be the ratio of Cats to dogs in the pet store?
Options:
A)1:3
B)1:4
C)1:5
D)2:5
E)68:85
Rationale: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.
We are told that ax - bx = 17 --> x(a - b) = 17. Since 17 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*17.
The above implies that either x = 1 and (a - b )= 17 or x = 17 anda - b = 1.
Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 17.
For the original question only option which fits is E, 4:5. Cats = 17*4 = 68 and dogs = 17*5 = 85.
Answer: E.
Answer: E
Question: 15 litres of mixture contains 25% alcohol and the rest water. If 3litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
Options:
A)20.83%
B)23%
C)18.3%
D)19.75%
E)21.23%
Rationale: Alcohol in the 15litres of mix. = 25% of 15litres = (25*15/100) = 3.75litres
water in it = 15-3.75 = 11.25litres
new quantity of mix. = 15+3 = 18 litres
Quantity of alcohol in it = 3.75litres
Percentage of alcohol in new mix. = 3.75*100/18 = 20.83%
Answer is A
Answer: A
Question: In 15 year’s time the combined age of my four brothers will be 107. What will it be in six year’s time?
Options:
A)65
B)87
C)71
D)60
E)66
Rationale: C
71
Combined age in 15 years = 107.
4 × 15 = 60, therefore combined age now is 107 – 60 = 47.
In 6 years time, therefore, combined age will be
47 + 24 (4 × 6) = 71.
Answer: C
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Options:
A)16299
B)1640
C)277
D)298
E)279
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025 = 1640
Answer:B
Answer: B
Question: Aravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he
take along with him?
Options:
A)2800
B)3000
C)3200
D)3400
E)3500
Rationale: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
B
Answer: B
Question: ((1^m)/(5^m))((1^17)/(4^17)) = 1/(2(10)^33)
What is m?
Options:
A)17
B)18
C)34
D)35
E)33
Rationale: ((1^m)/(5^m))((1^17)/(4^17)) = 1/(2(10)^33)
((1/5)^m ) * ((1/2)^34) = 1/ (2 * (2*5)^33))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^m= (1/5)^33
((1/5)^m ) * ((1/2)^34) = 1/[(2^34)*(5^33)]
So, m=33
Answer E
Answer: E
Question: If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is:
Options:
A)45%
B)23%
C)20%
D)60%
E)56%
Rationale: C
C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%
Answer: C
Question: The average age of 12 students is 20 years. If the age of one more student is included, the average decreases by 1, what is the age of the new student?
Options:
A)5
B)7
C)9
D)11
E)13
Rationale: Average age of 12 students is 20 years means sum of 12 students age is 240
If the age of one more student is included, the average decreases by 1, means 13 students age is 13*19 =247
Difference between 12 and 13 students is 7.
ANSWER:B
Answer: B
Question: Sahil purchased a machine at Rs 13000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.
Options:
A)Rs. 22000
B)Rs. 24500
C)Rs. 26500
D)Rs. 28500
E)None of these
Rationale: Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 13000 + 5000 + 1000 = 19000
150% of 19000 = 150/100 * 19000 = 28500
Option D
Answer: D
Question: A container contains 30 liters of milk. From this container 5 liter of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Options:
A)17.26liter
B)17.39 liter
C)17.36 liter
D)17.32 liter
E)57.36 liter
Rationale: Explanation:
No explanation is available for this question!
ANSWER:C
Answer: C
Question: Factor: 5x2 – 15x – 20
Options:
A)(a) 5(x-4)(x+1)
B)(b) -2(x-4)(x+5)
C)(c) -5(x+4)(x-1)
D)(d) 5(x+4)(x+1)
E)(e) 5(x-4)(x-1)
Rationale: 5x2 – 15x – 20.
= 5(x2 – 3x – 4).
= 5(x2 – 4x + x – 4).
= 5{x(x - 4) +1(x - 4)}.
= 5(x-4)(x+1).
the answer is (A)
Answer: A
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.
Options:
A)7/9
B)7/15
C)3/5
D)4/3
E)8/5
Rationale: let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45
Let E=event of getting both balls of same colour
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
Ans: B
Answer: B
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
Options:
A)111.12
B)111.16
C)111.15
D)111.19
E)111.18
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer: A
Answer: A
Question: The perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)28 cm2
B)27 cm2
C)29 cm2
D)25 cm2
E)35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 20/2
= 25 cm2
Answer: D
Answer: D
Question: An advertising agency finds that, of its 210 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?
Options:
A)56
B)70
C)90
D)110
E)120
Rationale: Total=210
Television=115
Radio=110
Magazine=130
All the three =210-115-110-130+85+75+95=110
ANSWER D
Answer: D
Question: How many multiples of 2 are there between 1 and 52, exclusive?
Options:
A)21
B)22
C)25
D)26
E)28
Rationale: 25
multiples of 2 between 1 and 52 exclusive.
from 2 * 1 upto 2*25, (1,2,3,4,...,25). Hence, 25 multiples !
correct option is C
Answer: C
Question: A day-trader plans to invest a total of $23,600 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment?
Options:
A)$2,800
B)$4,000
C)$3,500
D)$3,800
E)$3,900
Rationale: We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice).
Total of 14 minimized investments = (14)(1400) = $???600
The 15th investment + $???600 = $23,600
So, the HUNDREDS DIGITS of the 15th investment must be 0
Answer: B
Answer: B
Question: The value of x + x(xx) when x = 4 is:
Options:
A)A)36
B)B)16
C)C)18
D)D)68
E)E)10
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
4 + 4(44)
= 4 + 4(4 × 4)
= 4 + 4(16)
= 4 + 64
= 68
D
Answer: D
Question: Jim is able to sell a hand-carved statue for $660 which was a 20% profit over his cost. How much did the statue originally cost him?
Options:
A)$496.30
B)$512.40
C)$550
D)$574.90
E)$588.20
Rationale: Cost Price = 660/120 * 100 = 550
Answer : C
Answer: C
Question: In what ratio should a variety of rice costing Rs. 5.5 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Options:
A)5/6
B)5/9
C)5/1
D)5/8
E)7/6
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties
= x : y
By the rule of allegation, x/y
= (8.75 - 7.50) / (7.50 - 5.5) =5/8
Answer: D
Answer: D
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)299
B)240
C)277
D)255
E)143
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer:B
Answer: B
Question: If 20% of A is the same as 30% of B, then A : B is :
Options:
A)5:4
B)5:3
C)4:3
D)3:2
E)1:3
Rationale: Expl : 20% of A I= 30 % of B =20A/100 = 30B/100 = 3/2 = 3:2
Answer:D
Answer: D
Question: A certain university will select 1 of 8 candidates eligible to fill a position in the mathematics department and 2 of 12 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Options:
A)340
B)380
C)472
D)528
E)630
Rationale: 1C8*2C12 = 8*66 = 528
the answer is (D)
Answer: D
Question: At Peter's firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?
Options:
A)700
B)1000
C)1300
D)1600
E)2000
Rationale: At Peter's firm's annual revenue grows twice as fast as its costs.First solve for how much revenue is increasing each year:
R2008= R2007*(1+x)
R2009= R2007*(1+x)^2=1.44*R2007
(1+x)^2 = 1.44
1+x=1.2
x=0.2 aka revenue increases 20% each year and cost increases 10% annually
Next solve for R2007and C2007:
R2007= C2007- 1000
1.2*R2007- 1.1*C2007= 0
1.2*[C2007- 1000] - 1.1*C2007= 0
0.1*C2007= 1,200
C2007= 12,000
R2007= 11,000
Finally find 2009 profits:
Profit2009= 1.44*11,000 - 1.21*12,000
Profit2009= 15,840 - 14,520
Profit2009= 1320
Answer: C
Answer: C
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Options:
A)60 cm^2
B)30 cm^2
C)20 cm^2
D)40 cm^2
E)50 cm^2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2
ANSWER B
Answer: B
Question: The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
Options:
A)20
B)30
C)48
D)58
E)68
Rationale: Explanation:
Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 =5*3/5 : 8*3/5 =3: 24/5
A : B : C = 2 : 3 :	24/5=10:15:24
B =	98* 15/49 =30.
Answer IS B
Answer: B
Question: In a simultaneous throw of 2 dice what is the probability of getting a total of 5?
Options:
A)1/4
B)1/9
C)2/11
D)3/13
E)1/5
Rationale: n(S) = 6*6 = 36
E = {(1,4),(2,3),(3,2),(4,1)}
Probability = 4/36 = 1/9
Answer is B
Answer: B
Question: In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.835 per pound?
Options:
A)1:3
B)1:2
C)1:1
D)2:1
E)3:1
Rationale: Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.835
0.9 – 0.1x = 0.835
x = 0.65
Thus ratio of both flours is 2:1
D
Answer: D
Question: A man took some money for borrowed, for 3 years the total will be Rs.6500 and 5 years it will be Rs.7500/-. Then how much amount he borrowed?
Options:
A)s.5000/-
B)s.5500/-
C)s.5770/-
D)s.5800/-
E)s.5820/-
Rationale: 3 years --------> Rs.6500/-
5 years --------> Rs.7500/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.6500/- - Rs.1500/- = Rs.5000/-
P = Rs.5000/-
A
Answer: A
Question: The cost of an item was reduced from its usual selling price of $23.99 to $20.99. Which of the following is closest to the percent decrease in the price of the item?
Options:
A)12%
B)21%
C)24%
D)25%
E)42%
Rationale: The price decreased by 23.99 - 20.99 = $3.
$3 is a bit more than 12% of original price of $24.
Answer: A.
Answer: A
Question: Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 81, then which of the following can be a value of 2y + 3g?
Options:
A)52
B)-55
C)141
D)142
E)160
Rationale: 800score Official Solution:
First note that g can either be 9 or -9. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 9 and then g = -9. If g = 9, then x = 8/5. If g = -9, then x = -2. Since all of our solutions are whole numbers, we can dismiss 8/5. We use g = -9 and x = -2 to determine the value of y: y = 2(-9) + 4 = -14. Finally, we substitute the values for y and g into the last expression to determine its value : 2(-14) + 3(-9) = -28 - 27 = -55;the correct answer is (B).
Answer: B
Question: A certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water. If between 8 and 15 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately
Options:
A)3
B)4
C)7
D)8
E)9
Rationale: If sides are 7, vol=7^3=343
80%= 274.4, 85%=291.55
so vol above water, between 68.6 and 51.45 -->too big
If side are 4, vol = 64
80%=51.2, 85%=54.4
vol above water between 12.8 and 9.6
So 4 should be the answer.
Check option C,
If sides are 5, vol = 125
80%= 100, .85%=106.25
vol above water between 18.75-25
(Sides are 4 cubic centimeters)
B
Answer: B
Question: How many three digit numbers contain the digit 5 at least once?
Options:
A)52
B)128
C)252
D)648
E)900
Rationale: The question is basically asking how many numbers between 100-999 contain at least one digit as 5.
Let ABC be a 3 digit number A can be filled with 9 digits, B can be filled with 10 digits and C can be filled with 10 digits. (because hundredth digit can only be between 1-9= 9 digits)
Therefore total number of ways we can form 3 digit number=9*10*10=900 ways (100-999)
Number of ways we can form a 3 digit number without the digit 5= 8*9*9= 648 ways
ANSWER:D
Answer: D
Question: A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 5
II. 1
III. -5
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: The question is which of the following must be in the set, not could be in the set.
If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.
Answer: C.
Answer: C
Question: There are two decks of 10 cards each. The cards in each deck are labeled with integers from 11 to 22 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?
Options:
A)0.23
B)0.36
C)0.4
D)0.42
E)0.46
Rationale: If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:
11 = 11
12 = 2*2*3
13 = 13
14 = 7*2
15 = 5*3
16 = 2*2*2
17 = 17
18 = 3*2*3
19 = 19
20 = 5*2*2
Combos that have a 2 and a 3 as factors (first + second card):
12 + anything - 19 of these possibilities (we count 12 + 12 only once)
14 + 15 - 2 of these possibilities
15 + 16 - 2 of these possibilities
15 + 20 - 2 of these possibilities
18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities
Total possibilities that will be a multiple of 6: 42
Total possibilites: 10*10=100
Probability = 42/100 = 0.36
Answer:B
Answer: B
Question: A certain number successively divided by 2, 5 and 7 leaves remainders 1, 2 and 3 respectively. When the same number is divided by 70, what is the remainder?
Options:
A)33
B)34
C)35
D)36
E)37
Rationale: 2) 105 (52 5) 52 (10 7) 10 (1
104 50 7
-------- -------- - -----
1 2 3
=> 65
105/70 = 35 (Remainder)
ANSWER:C
Answer: C
Question: John can finish a job in 30 days. If he worked for 15 days alone before he was joined by Kennedy to complete the job in 3 days, how many days will it take both of them to complete the entire job?
Options:
A)4
B)3
C)5
D)6.5
E)6
Rationale: Explanation:
John and Kennedy complete half work in 3 days
=> they can complete whole work in 6 days
Answer: Option E
Answer: E
Question: SUMO,INC recently conducted a survey and found that 200,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of SUMO,INC customers live in urban areas ?
Options:
A)200,000
B)216,000
C)360,000
D)480,000
E)600,000
Rationale: Let's say that we have a starting value of X...
100% of X = X
100% MORE than X = X + X = 2X
200% MORE than X = X + 2X = 3X
300% MORE than X = X + 3X = 4X
Etc.
Here, we're told that 200,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...
3(200,000) = 600,000
Final Answer:E
Answer: E
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 175, how many coins of each type are there?
Options:
A)20 coins
B)30 coins
C)50 coins
D)100 coins
E)None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 175
⇒ 1.75x = 175 ⇒ x = 100 coins
Answer D
Answer: D
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)89.2 km/hr
B)79.9 km/hr
C)99.2 km/hr
D)79.2 km/hr
E)72.2 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5
= 79.2 km/hr.
Answer: D
Answer: D
Question: In a certain town, the ratio of NY Yankees fans to NY Mets fans is 2:1, and the ratio of NY Mets fans to Boston Red Sox fans is 3:7. If there are 320 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?
Options:
A)48
B)52
C)56
D)60
E)64
Rationale: The ratio of Yankees:Mets:Red Sox = 6:3:7
The Mets fans are 3/16 of the population.
(3/16)*320 = 60
The answer is D.
Answer: D
Question: There is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 14,000 after 3 years at the same rate?
Options:
A)2372
B)4634
C)4542
D)2343
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. 14000. T = 3 years and R = 10% p.a.
C.I.
= Rs. 14000 x 1 +	10 3	- 1
100
= Rs. 14000 x	331
1000
= 4634.
B
Answer: B
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2400 less than the principal. What was the principal?
Options:
A)1500
B)2500
C)2507
D)3000
E)11500
Rationale: P - 2400 = (P*5*4)/100
P = 3000
Answer: D
Answer: D
Question: Flat 40% discount. a girl buys jacket for 480. what is the marked price?
Options:
A)600
B)700
C)800
D)850
E)900
Rationale: 40% discount.. means buy on 60% Marked price.
then 480 is 60% of the marked price
480/60=8
8 is 1% of marked price
then 8*100=800
ANSWER:C
Answer: C
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 3m3 , then the rise in the water level in the tank will be:
Options:
A)20 cm
B)25 cm
C)35 cm
D)18.75 cm
E)None of these
Rationale: Explanation:
Total volume of water displaced =(3 x 50) m3 = 150 m3
Rise in water level = 150/40Ã—20= 0.1875m = 18.75cm
Answer: D
Answer: D
Question: In an examination amar got 8% less than the pass mark and mohan got 20% more than the pass mark. If the difference between the percentage of their mark is 14, then what is the pass percentage
Options:
A)40%
B)50%
C)60%
D)cannot be determined.
E)None of these
Rationale: Let P be the pass percentage, then
Amar got 0.92 P% and mohan got 1.2 p%
Given that, 1.2 P – 0.92 p = 14
P =14/0.28 = 50%
ANSWER:B
Answer: B
Question: If 8 goldsmiths, working 9 hours a day, can make 20 ornaments in 24 days, how many ornaments will 18 goldsmiths make in 36 days, each working 8 hours a day?
Options:
A)126
B)60
C)92
D)138
E)140
Rationale: Explanation :
(Goldsmiths 8: 18) : (His/Day 9:8 ) : (Days 24 : 36) : : 20 : x
8 * 9 * 24*x =18 * 8 * 36 * 20 or x = 60
Answer : B
Answer: B
Question: Susan, John, Daisy, Tim, Matt, Jane and Kim need to be seated in 7 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Options:
A)36
B)120
C)800
D)2400
E)2520
Rationale: Total # of arrangement of 7 people is 7!.
In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).
So, # of arrangements to satisfy the given condition is 7!/2=2520.
Answer: E.
Answer: E
Question: The successive discounts 20% and 15% are equal to a single discount of?
Options:
A)12%
B)45%
C)32%
D)98%
E)78%
Rationale: C
Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.
Answer: C
Question: A can do a piece of work in 80 days and B in 100 days. They work together for 20 days and then B goes away.In how many days will A finish the remaining work?
Options:
A)33 days
B)44 days
C)55 days
D)42 days
E)32 days
Rationale: Explanation:
In this type of questions we first get the finishing of work in 1 minute for both pipes then we will add them to get the result, as:
Part finished by A in 1 day= 1/80
Part finished by B in 1 day = 1/100
Part finished by (A+B) in 1 day = 1/80 + 1/100
= 9/400
So (A+B)'s 20 days work =20*9/400=9/20 Remaining work =1-9/20=11/20. Number days to finish the remaining work by A =80*11/20=44 days.
Option B
Answer: B
Question: The average of first five prime numbers greater than 17 is?
Options:
A)32.2
B)32.98
C)32.3
D)32.8
E)27.8
Rationale: 19 + 23 + 29 + 31 + 37
= 139/5
= 27.8
Answer: E
Answer: E
Question: Shanti's school normally FINISHES AT 4 PM. her mom drives from home to pick her up, reaching the school exactly at 4 pm. one day, a half holiday is announced and the School finishes for the day at 1 pm. Rather than sitting and Waiting , Shanti decides to start walking towards home. Her mother meets her along the way and as a result they reach home an hour earlier than normal. what is the ratio of the Shanti's walking speed to her mother's driving Speed?
Options:
A)1:2
B)1:3
C)1:4
D)1:5
E)1:6
Rationale: together they save 1hr, i.e, in a one way trip, they would save half Hour each.
therefore, instead of meeting Shanti at 4pm in the school, her mother meets her at 3.30pm(half an hour earlier, to & fro will save 1 hour)
Therefore from the meeting point, to reach the school, the car would take .5 hrs
However, Shanti took 2.5 hrs(3.30-1) to reach the meeting point
Therefore, .5 Times Mom's speed = 2.5 Times Shanti's speed----->(distance=time x speed, since distance is same, equating the product of time and speed for both the cases)
therefore, ratio of the speeds is 1:5
ANSWER:D
Answer: D
Question: A and B can together complete a piece of work in 4 days. If A can alone can complete the same work in 12 days, in how many days can B alone complete that work?
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: (A+B)'s 1 day work = 1/4
A's 1 day work = 1/12
B's 1 day work = 1/6
ANSWER A
Answer: A
Question: Tim's garden is shaped like a square whose side is 28 meters. What's the length of the fence which surrounds the garden?
Options:
A)110 meters
B)111 meters
C)112 meters
D)113 meters
E)114 meters
Rationale: Solution:
All sides of the square are equal. The length of the fence is 4 times the side. P = 4 × 28 = 112 meters
Answer C
Answer: C