subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | Calculate the percentage gain if a trader bought a bicycle for Rs.740 and sold it for Rs.1250? | [
"61.92%",
"68.92%",
"66.92%",
"63.92%",
"62.92%"
] | C.P. = 740
S.P. = 1250
Gain = 1250-740 ---- 510
% Gain => 510/740*100 => 68.92%
Answer:B
The answer is: B | B |
mathematics | A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train. | [
"182 km/hr",
"180 km/hr",
"152 km/hr",
"169 km/hr",
"179 km/hr"
] | Explanation:
Length of the train, l = 150m
Speed of the man , Vm= 2 km/hr
Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr
Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)
=> 180 = Vt - 2
=> Vt = 180 + 2 = 182 km/hr
Answer: Option A
The a... | A |
mathematics | What least number must be subtracted from 427398 so that remaining no.is divisible by 14 | [
"3",
"5",
"6",
"7",
"8"
] | Explanation:
On dividing 427398 by 14 we get the remainder 6, so 6 should be subtracted
Answer: Option C
The answer is: C | C |
mathematics | Find the length of the wire required to go 11 times round a square field containing 27889 m2. | [
"7348",
"3388",
"2667",
"8766",
"66711"
] | a2 = 27889 => a = 167
4a = 668
668 * 11 = 7348
Answer: A
The answer is: A | A |
mathematics | The present population of a town is 3888. Population increase rate is 20% p.a. Find the population of town before 2 years? | [
"2500",
"2100",
"3500",
"3600",
"2700"
] | P = 3888
R = 20%
Required population of town = P/(1 + R/100)^T
= 3888/(1 + 20/100)^2
= 3888/(6/5)^2
= 2700(approximately)
Answer is E
The answer is: E | E |
mathematics | Bhanu spends 30% of his income on petrol on scooter 12% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent? | [
"62",
"140",
"84",
"60",
"123"
] | Given 30% (Income ) = 300 ⇒⇒ Income = 1000
After having spent Rs.300 on petrol, he left with Rs.700.
His spending on house rent = 12% (700) = Rs.84
Answer:C
The answer is: C | C |
mathematics | 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? | [
"40",
"200",
"266",
"267",
"600"
] | 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.
The answer is: D | D |
mathematics | A plot is sold for Rs. 18,700 with a loss of 15%. At what price it should be sold to get profit of 15%? | [
"Rs 25300",
"Rs 22300",
"Rs 24300",
"Rs 21300",
"None of these"
] | Explanation :
This type of question can be easily and quickly solved as following:Let at Rs x it can earn 15% profit
85:18700 = 115:x [as, loss = 100 -15, Profit = 100 +15]x = (18700 X 115)/85
= Rs.25300
Answer : A
The answer is: A | A |
mathematics | A sum of money deposited at C.I. amounts to Rs.9000 in 10 years and to Rs.9990 in 11 years. Find the rate percent? | [
"9%",
"10%",
"11%",
"12%",
"13%"
] | 9000 --- 990
100 --- ? => 11%
Answer: C
The answer is: C | C |
mathematics | If a man lost 7% by selling oranges at the rate of 21 a rupee at how many a rupee must he sell them to gain 42%? | [
"12.75",
"11.75",
"8.75",
"15.75",
"13.75"
] | 93% ---- 21
142% ---- ?
93/142 * 21 = 13.75
Answer: E
The answer is: E | E |
mathematics | If the number is divided by 3, it reduced by 42. The number is | [
"A)51",
"B)63",
"C)45",
"D)40",
"E)36"
] | Explanation:
Let the number be x. Then,
x - (x/3) = 42 => 2x/3 = 42
=> x = 63
Answer: Option B
The answer is: B | B |
mathematics | At a conference table, 4 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these 4 employees? | [
"12",
"10",
"14",
"8",
"6"
] | Head's sit is fixed. Now 3 people is left with 3 seats.
3 people can sit on 3 seats in 3! ways or 6 ways.
Ans is E
The answer is: E | E |
mathematics | Amit and Ananthu can do a work in 10 days and 20 days respectively. Amit started the work and left after 2 days. Ananthu took over and completed the work. In how many days was the total work completed? | [
"18 days",
"20 days",
"23 days",
"25 days",
"27 days"
] | Amit’s one day’s work= 1/10
Amit’s 2 day’s work = 1/10 *2 = 1/5
Work left= 1-1/5 = 4/5
Ananthu’s one day’s work= 1/20
Ananthu can do work in = 4/5 *20 = 16 days
So total days = 16+2 = 18 days
ANSWER:A
The answer is: A | A |
mathematics | Find the greatest number which on dividing 4351 and 5161, leaves a reminder of 8 and 10 respectively | [
"125",
"111",
"129",
"101",
"141"
] | Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (4351 - 8) and (5161 -10)
= HCF (4343, 5151) = 101
Option D
The answer is: D | D |
mathematics | The mean of 50 observations is 200. But later he found that there is decrements of 34 from each observations. what is the the updated mean is ? | [
"165",
"166",
"190",
"198",
"199"
] | 166
Answer is B
The answer is: B | B |
mathematics | if ratio of total amount and principal amount is 3:2.rate of interest 5%.calculate the time. | [
"10",
"6",
"5",
"8",
"data not available"
] | s.i=p*r*t/100
(total amount-p)/p=5t/100
t.a/p-1=5t/100
1.5-1=5t/100
50=5t
t=10
answer A
The answer is: A | A |
mathematics | In the first 7 overs of a cricket game, the run rate was only 4.2. What should be the rate in the remaining 30 overs to reach the target of 282 runs? | [
"6.25",
"8.42",
"8.3",
"8.1",
"6.21"
] | Required run rate
= [282 - (4.2 * 7)]/30
= 252.60/40
= 8.42
Answer:B
The answer is: B | B |
mathematics | The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 10 terms of the arithmetic progression? | [
"300",
"100",
"150",
"170",
"270"
] | n th term of A.P. is given by a+(n-1)d
4 th term = a+3d
12 th term = a+11d
Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10
Sum of n term of A.P = n/2[2a+(n-1)d]
subsitiuing n = 10 ...we get 10/2[ 2a + 14d] = 10 [a+7d] = 10*10 = 100...
Answer is B...
The answer is: B | B |
mathematics | A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of three cubic feet. If a large block has twice the width, twice the depth, and three times the length of a normal block, what is the volume of cheese in a large block in cubic feet? | [
"18",
"6",
"27",
"48",
"36"
] | Volume of cube=lbh=3
New cube l ,b, h are increases of 3l,2b,2h
New volume of cube =3l*2b*2h=12lbh
=12*3
=36
Answer: E
The answer is: E | E |
mathematics | Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $760. How much more do pairs of boots cost than pairs of shoes at Suz... | [
"$2.50",
"$5.00",
"$5.50",
"$7.50",
"$15.00"
] | Let X be pair of shoes and Y be pair of boots.
22x+16y = 650 ... eq1
8x +32y = 760....eq 2.
Now multiply eq 1 by 2 and sub eq 2.
44x = 1300
8x = 760.
36x = 540 => x = 15.
Sub x in eq 2.... we get 120 + 32y = 760... then we get 32y = 640 then y = 20
Difference between X and Y is 5.
Answer: option B is correct answer.
Th... | B |
mathematics | A pharmaceutical company received $4 million in royalties on the first $24 million in sales of generic equivalent of one of its products and then $5 million in royalties on the next $60 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $24 million in sales to th... | [
"10%",
"20%",
"25%",
"30%",
"35%"
] | change in ratio of royalties to sales = 4/24 -5/60 = 1/12
% decrease = (1/12)/(4/24) *100 = 20%
Answer: B)
The answer is: B | B |
mathematics | A man can reach a certain place in 30 hours. If he reduces his speed by 1/15th, he goes 10 km less in that time. Find his speed. | [
"4 1/2km/hr",
"5 km/hr",
"5 1/2km/hr",
"6 km/hr",
"none"
] | Sol.
Let the speed be x km/hr. Then,
30x-30*14/15x = 10
⇔ 2x = 10
⇔ x = 10/2
= 5 km/hr
Answer B
The answer is: B | B |
mathematics | John makes $60 a week from his job. He earns a raise and nowmakes $70 a week. What is the % increase? | [
"16%",
"16.66%",
"17%",
"17.2%",
"18%"
] | Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
The answer is: B | B |
mathematics | Ratio between Rahul and Deepak is 4:3, After 2 Years Rahul age will be 26 years. What is Deepak present age. | [
"14",
"18",
"20",
"22",
"24"
] | Explanation:
Present age is 4x and 3x,
=> 4x + 2 = 26 => x = 6
So Deepak age is = 3(6) = 18
Option B
The answer is: B | B |
mathematics | What is the sum of the different positive prime factors of 620? | [
"17",
"24",
"38",
"47",
"62"
] | The prime factorization of 620
= 62 * 10
= 2*31 * 2*5
The sum of the different positive prime factors = 2+5+31 = 38
The answer is C.
The answer is: C | C |
mathematics | Find the fourth proportion to 11,12,66 | [
"80",
"120",
"90",
"25",
"72"
] | Explanation:
11:12 :: 66:x
=> 11/12 = 66/x
=> x = 792/11
=> x =72
Option E
The answer is: E | E |
mathematics | Two friends are making lemonade to sell at their lemonade stand. First, they make 14 litres of lemonade containing 21% lemon juice, but that doesn't taste quite right to them. They decide to add some store-bought lemonade that is 31% lemon juice until they have a mixture that is 25% lemon juice. How much of the store-b... | [
"6.6 litres",
"12 litres",
"9 litres",
"2.6 litres",
"9.3 litres"
] | 0.21(14)+0.31x = 0.25(14 + x)
Solve the equation.
0.21(14) + 0.31x = 0.25(14 + x)
2.94 + 0.31x = 3.5 + 0.25x
2.94 + 0.06x = 3.5
0.06x = 0.56
x ≈ 9.3
Answer is E.
The answer is: E | E |
mathematics | 2 dice are tossed. What is the probability that the total score is a prime no. is? | [
"1/13",
"5/12",
"3/11",
"4/13",
"5/13"
] | 5/12
B
The answer is: B | B |
mathematics | .
On dividing a number by 357, we get 36 as remainder. On dividing the same number 17, what will be the remainder ? | [
"0",
"3",
"5",
"8",
"2"
] | Let x be the number and y be the quotient. Then,
x = 357 x y + 36
= (17 x 21 x y) + (17 x 2) + 2
= 17 x (21y + 2) + 2)
Required remainder = 2.
Answer: Option E
The answer is: E | E |
mathematics | A circular rim 20 inches in diameter rotates the same number of inches per second as a circular rim 5 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ? | [
"48pi/x",
"75x",
"48x",
"240x",
"x/75"
] | Revolutions - circumference of the rim.
=> 20pi*X*60 = 5pi*Revolutions
=> 4/1 *X *60 = Revolutions => 240X - Option D
The answer is: D | D |
mathematics | The months of the calendar have been coded in the following ways:
January = 1071
February = 682
March = 1353
April = 154
May = 1335
June = 1046
July = 1047
August = 168
Using the same coding method, can you find out how to code September | [
"19|9|9",
"19|9|8",
"19|9|7",
"19|9|6",
"19|9|5"
] | Solution:
19|9|9
Explanation:
This is simple. All the months have been coded with a distinctive way.
Let's see about January:
January = 1071 = 10|7|1
10 is the position of J, the first letter of January in alphabetical order.
7 is the number of letters used in forming the word January.
1 is the position of January in t... | A |
mathematics | Find the average of all the numbers between 11 and 34 which are divisible by 10? | [
"10",
"20",
"25",
"30",
"15"
] | Average = (20+30) 2= 50/2 = 25
Answer is C
The answer is: C | C |
mathematics | 1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. | [
"$140",
"$125",
"$145",
"$135",
"$155"
] | Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
ANSWER : ... | C |
mathematics | The midpoints of three of the edges of a cube are
labelled A, B, and C as shown in the diagram. What
is the measure of L ABC ? | [
"90o",
"105o",
"120o",
"135o",
"150o"
] | Let D be the point on the base of the cube such that CD is perpendicular to
the base. Let s be the length of the sides of the cube. Then AB = BC = AD =
p
2s/2.
Using the Pythagorean Theorem in 4ADC, we get AC =
p
3s/
p2. By the Law of
Cosines AC2 = AB2 +BC2 −2AB · BC · cos(\ABC). We get cos(\ABC) = −1/2, so
L ABC = 120... | C |
mathematics | What are the chances you would pull an Ace or Heart from a well-shuffled deck of cards? | [
"1 of 4",
"4 of 12",
"1 of 13",
"4 of 13",
"1 of 52"
] | You must add the number of cards in each suit in the deck (13/52) to the number of aces of in the deck (4/52) and subtract the number of aces of hearts in the deck (1/52). This will give you the number of 16/52 which when the fraction is reduced will give you the answer of 4/13. Answer is D.
The answer is: D | D |
mathematics | An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.18522/- in 3 years at the same rate of interest. Find the rate percentage? | [
"5%",
"6%",
"7%",
"8%",
"9%"
] | The difference of two successive amounts must be the simple interest in 1 year on
the lower amount of money.
S.I = 18522/- - 17640/- = Rs. 882/-
Rate of interest = (882/17640) × (100/1) => 8820/1764 = 5%
Principal = Amount/(1 + R/100)n
= 17640/(1 + 5/100)2
= 17640/(21/20 × 21/20)
= 17640/(1.05 × 1.05)
= 17640/1.1025
= ... | A |
mathematics | Q is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can Q be? | [
"300,000",
"349,999",
"350,000",
"399,999",
"400,000"
] | Q 1,000,000-300,000=700,000 integers
700,000/2= 350,000 even integers.
350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.
350,001-2=349,999
B
The answer is: B | B |
mathematics | By selling 32 mangoes in a dollar, a man loses 40%. How many mangoes must he sell in a dollar to gain 20% profit? | [
"16",
"18",
"20",
"25",
"28"
] | This is a question that is much easier than it first appears. If you work with the percents directly, you can solve it very quickly. If the man sells 32 mangoes for a dollar, he loses 40%. That means he is at 60% of his cost (100% - 40% = 60%). We are trying to figure out how many mangoes he has to sell in order to mak... | A |
mathematics | 8 liters are drawn from a cask full of wine and is then filled with water. This operation is performed three more times . The ratio of the quantity of wine now left in cask to that of the water is 16:65. How much wine did the cask hold originally? | [
"12",
"24",
"36",
"42",
"56"
] | Let the quantity of wine in the cask originally be x liters
quantity of wine left in cask after 4 operations = x(1 - 8/x)^4 liters
x(1 - 8/x)^4 /x = 16/81
(1-8/x)^4 = (2/3)^4
x = 24
Answer is B
The answer is: B | B |
mathematics | Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L | [
"1/3.",
"1/2.",
"3.",
"2.",
"6."
] | Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 9 and L be 3, 9 - 3 = (9 + 3 )/2
C
The answer is: C | C |
mathematics | What annual installment will discharge a debt of Rs. 4600 due in 4 years at 10% simple interest? | [
"1000",
"1030",
"1100",
"None of these",
"1101"
] | Let the 1st installment = 100/-
It is 3yrs before due
IInd is 2yr before due
III3rd is 1yr before due
IVth is 0 yrs before due
On 1st installment interest will be paid for 3yrs
2nd installment interest will be paid for 2yrs
3rd installment interest will be paid for 1yr
4th installment interest will be paid for 0yr
Inte... | A |
mathematics | When two dice are rolled, what is the probability that the sum is either 7 or 11? | [
"1/4",
"1/9",
"4/3",
"3/9",
"2/9"
] | Total number of outcomes possible=36
Probability of getting sum of 7=6/36
Probability of getting sum of 11=2/36
probability that the sum is either 7 or 11=6/36+2/36=2/9
ANSWER:E
The answer is: E | E |
mathematics | If 4 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture? | [
"(4x + 2y)/5",
"(4x + 2y)/(x + y)",
"(4x + 2y)/(xy)",
"5(4x + 2y)",
"4x + 2y"
] | Total Cost = Weight(in pounds) * Price/pound;
To find Total cost/pound, Divide by total pounds.
Cost of Dried apricots = 4x;
Cost of prunes = 2y;
Cost per pound = (4x + 2y)/5;
Ans is (A).
The answer is: A | A |
mathematics | A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream? | [
"7 kmph",
"9 kmph",
"3 kmph",
"8 kmph",
"2 kmph"
] | Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph.Answer: D
The answer is: D | D |
mathematics | Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255 | [
"11",
"8",
"27",
"63",
"127"
] | Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong.
B
The answer is: B | B |
mathematics | At a certain conference, 78% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance? | [
"18.0%",
"62.0%",
"79.2%",
"86.67%",
"82.0%"
] | I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.
78% regestered at least 2 weeks and paid full fee.
10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.
90% *X=78% where X is the number o... | D |
mathematics | The greatest possible length which can be used to measure exactly the length 6m ,2m 85cm, 4m 95 cm is? | [
"25cm",
"101cm",
"56cm",
"42cm",
"15cm"
] | Required length = H.C.F of 600cm, 285cm, 495cm = 15cm
Answer is E
The answer is: E | E |
mathematics | If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 45. By how much do the two digits differ? | [
"3",
"4",
"5",
"6",
"7"
] | Given that (10a + b) - (10b + a) = 45 --> 9a - 9b =45 --> a - b = 5.
Answer: C.
The answer is: C | C |
mathematics | If 9 is a factor of 2y, then which of the following may not be an integer? | [
"6y/54 + 2y/3",
"(4y-18)/9",
"(2y+27)/9",
"(81-4y^2)/81",
"(2y-3)/3"
] | I got the right answer A after plugging in 18 for y.
While going through Kaplan's explanation, I couldn't understand the part about choice A.
"6y/54 + 2y/3 = 3/6 * 2y/9 + 2y/3.
Since 9 is a factor of 2y, 3 is also factor of 2y. So 2y/3 is an integer, as is 2y/9. But 3/6 = 1/2, so if 2y/9 is not even, the expression 3/6... | A |
mathematics | The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is : | [
"20",
"30",
"38",
"48",
"None of these"
] | A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 98
or 49x = 98 or x = 2
⇒ Second number = 15x = 15 × 2 = 30
Answer B
The answer is: B | B |
mathematics | Pipe A can fill a tank in 8 hours, pipe B in 16 hours and pipe C in 48 hours. If all the pipes are open,in how many hours will the tank be filled ? | [
"4.7",
"4.5",
"4.6",
"4.8",
"5"
] | 1/8+1/16+1/48=10/48=1/4.8. so 4.8 hrs
ANSWER:D
The answer is: D | D |
mathematics | What decimal fraction is 70 ml of a litre ? | [
".7",
".07",
".05",
"0.07",
"None of these"
] | Answer
Required fraction = 70/1000
= 7/100
= .07
Correct Option: B
The answer is: B | B |
mathematics | Jonah drove the first half of a 200-mile trip in x hours and the second half in y hours. Which of the following is equal to Jonah’s average speed, in miles per hour, for the entire trip? | [
"100/(x + y)",
"200/(x + y)",
"25/x + 25/y",
"50/x + 50/y",
"100/x + 100/y"
] | Time taken by Jonah to cover first half i.e 100 miles of a 200 mile trip = x
time taken by Jonah to cover the second half i.e 100 miles of a 200 mile trip = y
Total time taken by Jonah = x+y
Jonah's average speed for the entire trip =total distance /total time
=200/(x+y)
Answer B
The answer is: B | B |
mathematics | A certain club has 8 members, including Harry. One of the 8 members is to be chosen at random to be the president, one of the remaining 7 members is to be chosen at random to be the secretary, and one of the remaining 6 members is to be chosen at random to be the treasurer. What is the probability that Harry will eithe... | [
"1/4",
"2/4",
"3/4",
"1",
"5/4"
] | Each member out of 8, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/8 and the probability that Harry will be selected to be the treasurer is also 1/8. So, the pr... | A |
mathematics | If 3y + x > 2 and x + 2y <= 3 , What can be said about the value of y? | [
"y = 1",
"y >1",
"y > -2",
"y > -1",
"None of these"
] | Explanation :
3y + x > 2 -----(1)
x + 2y < = 3
=> x + 2y + y < = 3 + y
=> x + 3y < = 3 + y -----(2)
From (1)&(2)
2 < 3y + x < 3 + y
=> 2 < 3 + y
=> -1 < y
=> y > -1
Hence (D) is the correct answer.
Answer : D
The answer is: D | D |
mathematics | Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and... | [
"1/10",
"3/20",
"1/5",
"1/4",
"9/20"
] | First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:
m + p + c = 20 (since 4/5 of the 25 spots are full of books)
m = 2p
p = 4 + c
From that, you can use Substitution to get everything down to one variable.
c = p - 4
m = ... | E |
mathematics | The admission charge in a water park is $1 by adult and $0.75 by child accompanying an adult.
How much was there of child with an adult who paid in quite $3.25 to have access to the water park? | [
"1",
"2",
"3",
"4",
"5"
] | a = # of adults Price for on adult = $1.00
e = # of kids Price for on kid (accompanying an adult) = $0.75
t = total ($) $3.25
t = Price for an adult*a + Price for on kid * e
3.25 = $1*a + $0.75*e
3.25 = a + $0.75*e
Because the kids have to be accompanying by an adult, a = 1
$3.25 = 1 + $0.75*e
$3.25 - 1 = 1 - 1 + $0.75... | C |
mathematics | A part-time employee’s hourly wage was increased by 10%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased? | [
"9%",
"15%",
"25%",
"50%",
"100%"
] | Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 10% wage increase, the employee makes $1.10/hour
We want the employee's income to remain at $100/week.
So, we want ($1.10/hour)(new # of hours) = $100
Divide both sides by 1.10 to get:
new # of hour... | A |
mathematics | Find the fourth proportional to 33.6 , 41.2 and 48.9? | [
"59.96",
"56.15",
"52.39",
"58.96",
"57"
] | Formula= Fourth proportional =(b x c)/a
a=33.6 , b=41.2 and c=48.9
(41.2 x 48.9)/33.6=59.96
A
The answer is: A | A |
mathematics | The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constan... | [
"1/72",
"1/36",
"1/18",
"1/12",
"1/9"
] | Its an AP question .... it is given clearly in the question .
Let the smallest angle be a
and the circle has 8 sectors and hence 8 angle with a common difference d
hence all the angles can be written in AP form with Cd as d ,
a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,
given that a+7d = 80 --------1
also
a + a+d + a+2d... | D |
mathematics | 8 friends went to a hotel and decided to pay the bill amount equally. But 7 of them could pay Rs. 80 each as a result 8th has to pay Rs. 70 extra than his share. Find the amount paid by him. | [
"140",
"121",
"110",
"160",
"None"
] | Explanation:
Average amount paid by 7 persons = Rs. 80
Increase in average due to Rs. 70 paid extra by the 8th men = Rs. 70/7= Rs. 10
Therefore, Average expenditure of 8 friends = Rs. 80 + Rs. 10 = Rs. 90
Therefore, Amount paid by the 11th men = Rs. 90 + Rs. 70 = Rs. 160
Correct Option: D
The answer is: D | D |
mathematics | courtyard 3.78 meters long 5.95 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose? | [
"22",
"77",
"877",
"99",
"88"
] | 3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7
5.25 meters=525 cm = 5 × 5 × 3 × 7
Hence common factors are 3 and 7
Hence LCM = 3 × 7 = 21
Hence largest size of square tiles that can be paved exactly with square tiles is 77 cm.
Answer:B
The answer is: B | B |
mathematics | A circular well with a diameter of 6 metres , is dug to a depth of 24 metres. What is the volume of the earth dug out? | [
"678.6 m3",
"36 m3",
"40 m3",
"44 m3",
"None"
] | Solution
Volume = πr2h
‹=› (22 /7 ×3×3×24)m3
‹=›678.6 m3.
Answer A
The answer is: A | A |
mathematics | The sum of the numbers is 177. If the ratio between the first and the second be 5:3 and that between the second and third be 4:9, then find the second number? | [
"12",
"20",
"45",
"60",
"52"
] | Given ratios
5 : 3
4 : 9
20:12:27
The second number = 177/(20+12+27) * 15 = 45
Answer is C
The answer is: C | C |
mathematics | The sum of three numbers is 294. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is : | [
"20",
"30",
"38",
"90",
"None of these"
] | A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 294
or 49x = 294 or x = 6
⇒ Second number = 15x = 15 × 6 = 90
Answer D
The answer is: D | D |
mathematics | How many quarters are equal to 7 dollars? | [
"1",
"28",
"12",
"9",
"7"
] | 7 * 4 = 28 quarters
Answer : B
The answer is: B | B |
mathematics | In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 5 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet? | [
"168.",
"80.",
"56.",
"48.",
"64."
] | Bed = Select 1 out of 4 = 4C1 = 4
Shelf = Select 1 out of 2 = 2C1= 2
Chair (5)+ Closet (3) = Total 8 = Select 1 out of 8 = 8C1
Possible combinations to chooseBED*SHELF*(CHAIR+CLOSET)=4*2*8=64 ways
ANSWER IS E
The answer is: E | E |
mathematics | Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? | [
"Rs.530",
"Rs.540",
"Rs.550",
"Rs.560",
"Rs.570"
] | A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
B
The answer is: B | B |
mathematics | A circle circumscribes three unit circles that touch each other. What is the area of the larger circle? Note that p is the ratio of the circumference to the diameter of a circle ( 3.14159265). | [
"3.14×(7+43–√3/9)",
"3.14×(7+43–√3/7)",
"3.14×(7+43–√3/6)",
"3.14×(7+43–√3/3)",
"3.14×(7+43–√3/1)"
] | By joining centers of 3 unit circles we will get an equilateral triangle of length 2 unit. We have to find the length of the orange line.
And center of the equilateral triangle will be the center of the big circle.
So radius of the big circle will be = (1 + Circum radius of the equilateral triagle)
Formula for Circul r... | D |
mathematics | Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days? | [
"Rs.1104",
"Rs.1000",
"Rs.934",
"Rs.1210",
"Rs.1410"
] | Explanation :
Assume that cost of keeping a cow for 1 day = c ,
cost of keeping a goat for 1 day = g
Cost of keeping 20 cows and 40 goats for 10 days = 460
Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46
=> 20c + 40g = 46
=> 10c + 20g = 23 ---(1)
Given that 5g = c
Hence equation (1) can be written as 10c +... | A |
mathematics | If J and X are integers, and 10J + X is odd, which of the following must be true? | [
"J is odd",
"J is even",
"X is odd",
"X is even",
"both J and X are odd"
] | 10J will be always even as 10 has 2 as one of its factors
if 10J+X is odd, then the only possible explanation is that X is odd
correct answer C
The answer is: C | C |
mathematics | What is the least possible value of expression E = (x-1)(x-3)(x-4)(x-6)+10 for real values of x? | [
"1",
"10",
"9",
"0",
"8"
] | Explanation :
E = (x-1)(x-6)(x-3)(x-4)+10
E = (x2-7x+6)(X2-7x+12)+10
Let x2-7x+6 = y
E = y2+6y+10
E = (y+3)2 + 1
Minimum value = 1 , when y = -3
Answer : A
The answer is: A | A |
mathematics | In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 2/5.
The probability of drawing a green ball is 7/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar? | [
"12",
"15",
"23",
"7",
"5"
] | answer of 1st
just add the given probabilities p(blue)+p(red)+p(green) i.e
1/8+2/5+ 3/10=5+16+12/40
now we know p(blue)+p(red)+p(green)+p(yellow)=1
33/40+p(yellow)=1
p(yellow)=33/40
i.e why yellow balls are 7.
D
The answer is: D | D |
mathematics | If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C? | [
"9:6:6",
"9:7:4",
"9:6:6",
"9:6:4",
"9:3:4"
] | A:B = 1/2:1/3 = 3:2
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:6:4
Answer: D
The answer is: D | D |
mathematics | A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price? | [
"250",
"277",
"255",
"278",
"281"
] | CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer: A
The answer is: A | A |
mathematics | n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1800, then what is the smallest possible value of n? | [
"8",
"10",
"12",
"15",
"18"
] | 1800=2^3*3^2*5^2
5^2 means that n must be at least 10. That is, We need 5 and 10.
The answer is B.
The answer is: B | B |
mathematics | Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. | [
"398",
"88",
"960",
"781",
"2891"
] | 60(x + 1) = 64x
X = 15
60 * 16 = 960 km.Answer:C
The answer is: C | C |
mathematics | The standard serial numbers for medical licence are 3 letters followed by 5 digits. How many different medical licenses are possible if letters and digits can be repeated? | [
"26 × × 3 × 5",
"26³ × 10 000",
"26³ x 100 000",
"26 × 25 × 24 × 10 × 9 × 8 × 7",
"26³ × 10 000 x 15"
] | OFFICIAL SOLUTION:
(C) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 × 26 options for the three letters, and 10 × 10 × 10 × 10 x 10 for the five digits. The number of different Medical license is 26 × 26 × 26 × ... | C |
mathematics | Of 45 applicants for a job, 21 had at least 4 years' experience, 27 had degrees, and 5 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree? | [
"6",
"8",
"4",
"3",
"2"
] | 45 - 5 = 40
40 - 21 - 27 = -8
Then 8 are in the intersection between 4 years experience and degree.
Answer : B
The answer is: B | B |
mathematics | In a jar there are 20 white balls, 24 green balls and 30 blue balls. How many balls must be taken out in order to make sure we have 21 balls of the same color? | [
"a)\t23",
"b)\t46",
"c)\t57",
"d)\t60",
"e)\t67"
] | Here, we need to find minimum number of marbles to be taken out to get 21 marbles of same color.
For a instance, if we take 19 white marbles 1st and followed by 20 Green and then 20 Blue.
Total will be 19 + 20+ 20= 59 draws.
If we choose either Green or Blue next time. This will bring the total of either of these color... | D |
mathematics | A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 5 employees to 2 different offices? | [
"30",
"32",
"31",
"33",
"35"
] | Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2*2=2^5=32.
Answer: B.
The answer is: B | B |
mathematics | If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions R represents the final price of the item? | [
"R=(10,000z + 100z(x – y) – xyz)/10,000",
"R=(10,000z + 100z(y – x) – xyz)/10,000",
"R=(100z(x – y) – xyz)/10000",
"(100z(y – x) – xyz)/10000",
"10000 /(x – y)"
] | -A-
z=Original Price
x=MU
y=MD
New price with MU:
z(x/100+1)
New price with MD:
z[(x/100+1)(-y/100+1)]
Solving…
=z[((x+100)/100)((-y+100)/100)]
=z(x100-xy+10000-100y)/10000
=(zx100-xyz+10000z-100yz)/10000 --> similar to A
The answer is: A | A |
mathematics | A group of men decided to do a work in 8days, but 3 of them became absent. If the rest of the group did the work in 10days, Find the original number of men? | [
"15",
"20",
"30",
"25",
"18"
] | Original number of men = 3*10 / (10-8) = 15
Answer is A
The answer is: A | A |
mathematics | An assembly line produces 15 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whol... | [
"20",
"22",
"24",
"26",
"28"
] | The time to produce the first 60 cogs is 60/15 = 4 hours.
The time to produce the next 60 cogs is 60/60 = 1 hour.
The average output is 120 cogs / 5 hours = 24 cogs per hour.
The answer is C.
The answer is: C | C |
mathematics | A chemist mixes one liter of pure water with x liters of a 40% salt solution, and the resulting mixture is a 20% salt solution. What is the value of x? | [
"1/4",
"1/3",
"1/2",
"1",
"3"
] | Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 40%
Concentration of salt in the mixed solution = 20%
The pure solution and the salt solution is mixed in the ratio of --> (40 - 20)/(20 - 0) = 1/1
1/x = 1/1
x = 1
Answer: D
The answer is: D | D |
mathematics | A table is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage | [
"25% gain",
"20% gain",
"20% loss",
"15% gain",
"None"
] | Formula = (Selling price ~ Cost price)/Cost price * 100
= (500 - 400)/400 = 25% gain
A
The answer is: A | A |
mathematics | For a right angle triangle the hypotenuse is 5 and base is 3. What is the area of the triangle? | [
"6",
"7",
"8",
"9",
"10"
] | As we know that for a right angle triangle the are is 1/2 * base * height
We know the base = 3
We need to calculate the height
hypotenuse = h = 5
base = b = 3
height = c = ?
As per Pythagoras
h^2 = b^2 + c^2
5^2 = 3^2 + c^2
25 = 9 + c^2
C^2 = 25 - 9
c^2 = 16
c = 4
height = 4
area = 1/2 * base * height
= 1/2 * 3 * 4
= 6... | A |
mathematics | Express a speed of 56 kmph in meters per second? | [
"10.56 mps",
"17.56 mps",
"97.56 mps",
"15.56 mps",
"18.56 mps"
] | 56 * 5/18
= 15.56 mps
Answer: D
The answer is: D | D |
mathematics | NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days they completed 1/3 part of work .than how many more employees should NHAI hire to finish it in time working 10 hours a day? | [
"22",
"60",
"28",
"11",
"218"
] | Here 2km is immaterial. The given problem can be written in a tabular form like below.
We can apply chain rule now.
Total men required to complete the remaining work = 100×2525×810×2313100×2525×810×2313 = 160
So additional men required = 160 - 100 = 60
Answer:B
The answer is: B | B |
mathematics | What is the 20th digit to the right of the decimal point in the decimal expansion of 1/37? | [
"0",
"2",
"4",
"7",
"9"
] | 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (2nd, 4th, 6th, ...) to the right of the decimal point is alternating by 2, 0, 7 thus 20th digit is 2.
Answer: B.
The answer is: B | B |
mathematics | A man walked a certain distance south and then the same distance plus 7km due west.He is now 13km from his starting point.What are the distances south and west that he walked? | [
"5,12",
"6,12",
"7,12",
"5,13",
"6,13"
] | If a man walked distance(in km) 'x' towards south & then 'x+7'towards west.
Distance from starting point=Hypotenuse of a right triangle with sides x & (x+7)
So 13^2=x^2+(x+7)^2
x^2+7x-60=0 or (x+12)(x-5)=0, so x=5
Distance towards west=x+7=5+7=12 km.
ANSWER:A
The answer is: A | A |
mathematics | In what ratio should a variety of rice costing Rs. 6.5 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? | [
"5/6",
"5/9",
"5/4",
"5/3",
"7/6"
] | 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 - 6.5) =5/4
Answer: C
The answer is: C | C |
mathematics | Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages | [
"65 years",
"35 years",
"55 years",
"44 years",
"11 years"
] | Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ lO) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years.
Answer: B
The answer is: B | B |
mathematics | Given that 0 < a < b < c < d, which of the following the largest ? | [
"(c+d) / (a+b)",
"(c+d) / (a+j)",
"(c+d) / (k+b)",
"(c+d) / (g+b)",
"(c+d) / (a+s)"
] | Explanation: Take a = 1, b = 2, c = 3, d = 4. option A is clearly true.
Answer:A
The answer is: A | A |
mathematics | The mass of 1 cubic meter of a substance is 100 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters) | [
"8",
"9",
"10",
"11",
"12"
] | 100 kg - 1 cubic meter;
100,000 g - 1 cubic meter;
100,000 g - 1,000,000 cubic centimeters;
1 g - 1,000,000/100,000 = 10/1 = 10 cubic centimeters.
Answer: C.
The answer is: C | C |
mathematics | Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 100 players took part in that tournament.
How many matches were played? | [
"99 matches",
"79 matches",
"69 matches",
"99 matches",
"59 matches"
] | D
99 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 99 matches were played.
The answer is: D | D |
mathematics | Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 60 percent of those who attended the meeting were stockholders and 47 percent were employees, what percent were stockholders who were not employees? | [
"53",
"54",
"55",
"56",
"57"
] | 60+47=107 so 7% were both stockholders and employees.
The percent who were stockholders but not employees is 60-7=53%
The answer is A.
The answer is: A | A |
mathematics | If 2a = 4b = 10, then 40ab = | [
"50",
"100",
"250",
"450",
"500"
] | 2a * 4b = 10 * 10 = 100
8 ab = 100
i.e. 40 ab = 500
Answer: Option E
The answer is: E | E |
mathematics | The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group? | [
"22",
"27",
"15",
"77",
"16"
] | Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs. 15.
Answer: C
The answer is: C | C |
mathematics | The smallest number which when divided by 20, 25, 35, 40 leaves the remainder 6 When divided by
14, 19, 23 and 34 respectively is the difference between divisor and The corresponding remainder is 6. | [
"1396",
"1394",
"1494",
"1384",
"1391"
] | The smallest number which when divided by 20, 25, 35, 40 leaves the remainder 6 When divided by
14, 19, 23 and 34 respectively is the difference between divisor and The corresponding remainder is 6.
= 1400-6 = 1394
Answer is B
The answer is: B | B |
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