subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marb... | [
"90",
"180",
"360",
"540",
"720"
] | # ways to distribute Blue marbles(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute Red marbles(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute Green marbles(1) is :
3 ways
total number of ways = 10*6 *3 ... | B |
mathematics | Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 78 minutes. The waste pipe can empty the full cistern in? | [
"8 min",
"7 min",
"5 min",
"9 min",
"6.5 min"
] | 1/10 + 1/15 - 1/x
= 1/78
x = 6.5
Answer:E
The answer is: E | E |
mathematics | A dealer professing to sell his goods at cost price, uses 900gm weight for 1 kg. His gain percent is | [
"13%",
"12 1/3%",
"11 1/9%",
"10%",
"12%"
] | Gain % = ( Error/ (( True value) - Error)) *100 %
= (1000gm -900gm) / (1000 -100)* 100 %
= 100/900*100%
= 100/9
= 11 1/9 %
ANSWER:C
The answer is: C | C |
mathematics | If E is the product of all positive integers less than 31, than what is the greatest integer k for which E/18^k is an integer? | [
"3",
"6",
"7",
"14",
"26"
] | 30!E must be divisible by (3*3*2)^k.
As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).
Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.
3 6 9*
12 15 18*
21 24 27**
30
Th... | C |
mathematics | The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? | [
"27",
"55",
"31",
"34",
"35"
] | The total of seven numbers = 7X22 = 154
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (154 - 99 ) = 55
B
The answer is: B | B |
mathematics | Two trains are running in opposite directions with the same speed. If the length of each train is 250 m and they cross each other in 10 sec, then the speed of each train is? | [
"30",
"31",
"36",
"25",
"90"
] | Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (250 + 250)/10 => x =25
Speed of each train = 25 m/sec.
= 25 * 18/5 =90 km/hr.
Answer: Option E
The answer is: E | E |
mathematics | A candidate got 31% of the votes polled and he lost to his rival by 2451 votes. How many votes were cast? | [
"6150",
"6250",
"6350",
"6450",
"6550"
] | Let x be the total number of votes.
0.31x + 2451 = 0.69x
0.38x = 2451
x = 2451/0.38 = 6450
The answer is D.
The answer is: D | D |
mathematics | What is the smallest five digit number that is divisible by 16, 36, 40, and 54? | [
"10200",
"10500",
"10800",
"11000",
"11400"
] | 16 = 2^4
36 = 2^2 * 3^2
40 = 2^3 * 5
54 = 2 * 3^3
LCM = 2^4 * 3^3 * 5 = 2160
The smallest five-digit number that is a multiple of 2160 is 5*2160 = 10,800
The answer is C.
The answer is: C | C |
mathematics | Which of these lines in the xy-plane does not contain any point with two negative coordinates? | [
"y = 4x",
"y = x + 6",
"y = x^2 - 5",
"y = x^3 + 3x",
"y = 2x^4"
] | 2x^4 is 0 when x is 0 and positive for all other values of x.
The answer is E.
The answer is: E | E |
mathematics | The greatest common factor of positive integers m and n is 14. What is the greatest common factor of (2m^2, 2n^2)? | [
"14",
"28",
"196",
"392",
"784"
] | m = 14j and n = 14k, where the greatest common factor of j and k is 1.
2m^2 = 2*14*14*j^2 and 2n^2 = 2*14*14*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*14*14 = 392
The answer is D.
The answer is: D | D |
mathematics | Convert the following unit:
6.5 hectares in m² | [
"55000 m²",
"80000 m²",
"70000 m²",
"67500 m²",
"65000 m²"
] | 6.5 hectares in m²
1 hectare = 10000 m²
Therefore, 6.5 hectares = 6.5 × 10000 m²
= 65000 m²
ANSWER : OPTION E
The answer is: E | E |
mathematics | Of the 120 passengers on Flight 750, 55% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class? | [
"44",
"48",
"50",
"52",
"58"
] | Number of passengers on flight = 120
Number of female passengers= .5*120 = 66
Number of passengers in first class = (10/100)* 120 = 12
Number of passengers in coach class = (90/100)* 120 = 108
Number of male passengers in first class = 1/3 * 12 = 4
Number of female passengers in first class = 12-4 = 8
Number of female ... | E |
mathematics | Mary's income is 60% more Than Tim's income and Tim's income is 10% less than Juan's income.What % of Juan's income is Mary's income. | [
"144%",
"B.120%",
"96%",
"80%",
"64%"
] | Even I got 96%
J = 100
T = 100*0.9 = 90
M = 90*1.6 = 144
If Mary's income is x percent of J
M = J*x/100
x = M*100/J = 144*100/100 = 144
Ans:A
The answer is: A | A |
mathematics | The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 150 square centimeters, what is the length of the rectangle in centimeters? | [
"15",
"16",
"17",
"18",
"19"
] | Perimeter = 2(W+L) = 5W
3W = 2L
W = 2L/3
WL = 150
2L^2/3 = 150
L^2 = 225
L = 15 cm
The answer is A.
The answer is: A | A |
mathematics | A contract is to be completed in 46 days sad 117 men were said to work 8 hours a day. After 33 days, (4/7) of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day? | [
"91",
"87",
"85",
"81",
"None of them"
] | Remaining work = (1-(4/7) =(3/7)
Remaining period = (46 - 33) days = 13days
Let the total men working at it be x.
Less work, Less men (Direct Proportion)
Less days, More men (Indirect Proportion)
More Hours per Day, Less men (Indirect Proportion)
Work (4/7): (3/7)
Days 13:33 } : : 117: x
Hrs/day 9 : 8
Therefore (4/7) x... | D |
mathematics | What is the smallest positive perfect square that is divisible by 9, 21, and 49? | [
"225",
"324",
"441",
"529",
"900"
] | The number needs to be divisible by 3^2, 3*7, and 7^2.
The smallest such perfect square is 3^2*7^2 = 441
The answer is C.
The answer is: C | C |
mathematics | In what time will a train 60 m long cross an electric pole, it its speed be 144 km/hr? | [
"2.5 sec",
"2.8 sec",
"7.5 sec",
"2.3 sec",
"1.5 sec"
] | Speed = 144 * 5/18
= 40 m/sec
Time taken = 60/40
= 1.5 sec.
Answer:E
The answer is: E | E |
mathematics | A grocer has a sale of Rs. 6345, Rs. 6927, Rs.6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? | [
"Rs. 3000",
"Rs. 4991",
"Rs. 5991",
"Rs. 6001",
"NOne"
] | Sol.
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562)
= Rs. 34009.
∴ Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer B
The answer is: B | B |
mathematics | A statue is being carved by a sculptor. The original piece of marble weighed 200 kg. In the first week 20 percent is cut away. In the second week 25 percent of the remainder is cut away. In the third week the statue is completed when 35 percent of the remainder is cut away. What is the weight of the final statue? | [
"97.5 kg",
"103 kg",
"108 kg",
"125 kg",
"117 kg"
] | A
97.5 kg
250 × 0.8 × 0.75 × 0.65 = 97.5 kg.
The answer is: A | A |
mathematics | What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad? | [
"814",
"800",
"100",
"200",
"456"
] | Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles = (1517 x 902)/41 x 41 = 814.
Answer:A
The answer is: A | A |
mathematics | In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is | [
"86",
"90",
"92",
"94",
"96"
] | Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86.
A
The answer is: A | A |
mathematics | In how many ways can the integer 800 be expressed as a product of two different positive integers? | [
"10",
"7",
"5",
"4",
"2"
] | 800=(2^5)*(5^2)
Since 800 is not a perfect square, no of ways=7
Answer B
The answer is: B | B |
mathematics | When a certain number X is divided by 61, the remainder is 24. What is the remainder when X is divided by 5? | [
"2",
"3",
"4",
"5",
"6"
] | When a certain number X is divided by 61, the remainder is 24. What is the remainder when X is divided by 5?
Putting a value say x = 24 we get remainder as 24 when divided by 61.
When 24 divided by 5 we get 4 as remainder.
C is the answer.
The answer is: C | C |
mathematics | Find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1:2? | [
"1:2",
"2:3",
"2:9",
"2:1",
"2:2"
] | 1:2
Answer: A
The answer is: A | A |
mathematics | Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? | [
"444 km",
"400 km",
"450 km",
"500 km",
"550 km"
] | 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
ANSWER A
The answer is: A | A |
mathematics | Which of the following expressions CAN be equal to 0 when x^2 −16= 0 ? | [
"x^2 − 6x + 9",
"x^2 − 4x + 3",
"x^2 − x − 2",
"x^2 − 7x + 6",
"x^2 − 5x + 4"
] | x^2 − 16 = 0
x=-4 or x=4
Onle one choice results in a possibility of 0 when you plug in -4 or 4 for x except rest of all
x^2 − 5x + 4
Answer is E
The answer is: E | E |
mathematics | When positive integer x is divided by positive integer y, the result is 59.32. What is the sum E of all possible 2-digit remainders for x/y? | [
"560",
"616",
"672",
"728",
"784"
] | ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
E=8(2+3+4....+12)=616.B
The answer is: B | B |
mathematics | The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is: | [
"480",
"520",
"600",
"960",
"840"
] | T.D. = B.G. x 100 / Rate x Time
= Rs.(24 x 100/10 x 2)= Rs. 120.
P.W. =(100 x T.D./Rate x Time)
= Rs.(100 x 120/10 x 2)= Rs. 600.
Correct answer is C.
The answer is: C | C |
mathematics | When the price of sugar was increased by 32%, a family reduced its consumption in such a way that the expenditure on sugar was only 10% more than before. If 30 kg were consumed per month before, find the new monthly consumption. | [
"20 kg",
"25 kg",
"30 kg",
"35 kg",
"None of these"
] | Since, expenditure = price × consumption
∴ 110% of 30 = 132⁄100 × new consumption
⇒ 110⁄100 × 30 = 132⁄100 × new consumption
⇒ New consumption = 25 kg
Answer B
The answer is: B | B |
mathematics | A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 36490
. What percentage of profit did he make? | [
"64%",
"49%",
"40%",
"70%",
"90%"
] | The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 36490
Profit(%) = (36490 - 22250)/22250 * 100
= 64%
Answer:A
The answer is: A | A |
mathematics | In how many ways can a group of 5 men and women be made out of a total of 7 men and 3 women? | [
"63",
"90",
"126",
"45",
"135"
] | Required number of ways=7c5 x 3c2
=7c2 x 3c1
=63
ANSWER A 63
The answer is: A | A |
mathematics | A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? | [
"288",
"277",
"120",
"285",
"121"
] | Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
The answer is: C | C |
mathematics | Jack spent 1/6 of his lifetime in adolescence. His facial hair started growing after 1/12 more of his life. He successfully married his girlfriend Diana after 1/7 more of his life. Their son was born after 5 years from then. The son lived just 1/2 of what Jack lived. Jack dies four years after his son died.
How long di... | [
"75",
"90",
"45",
"80",
"84"
] | E
84
Explanation:
Let us assume that jack lived for p years.
p/6 + p/12 + p/7 + 5 + p/2 + 4 = x
=> p = 84.
Therefore, Jack lived for 84 years.
The answer is: E | E |
mathematics | John completes a piece of work in 320 days, Rose completes the same work in 480 days. If both of them work together, then the number of days required to complete the work is? | [
"190",
"192",
"194",
"196",
"198"
] | If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 320 × 480/800 = 192 days
Answer is B
The answer is: B | B |
mathematics | The area of a rectangle is x2 + 4x -12. What are the dimensions of the rectangle (length and width)? | [
"x + 6 , x + -2",
"x + 7 , x + -2",
"x + 8 , x + -2",
"x + 9 , x + -2",
"none"
] | Solution
The main idea is to factor x2 + 4x -12
Since -12 = -2 × 6 and -2 + 6 = 4
x2 + 4x -12 = ( x + -2) × ( x + 6)
Since the length is usually longer, lenth = x + 6 and width = x + -2
Answer A
The answer is: A | A |
mathematics | In a shop, the marked price of an article is worked out in such a way that it generates a profit of 33133313. What should be the discount percent allowed on the marked price during a sale, so that the final profit made is 20%? | [
"13 1/3",
"12 1/2",
"10%",
"8 1/2",
"6 2/3"
] | soln:-
lets consider the cost price of an article as $60 (take a number whose 33.33% can be calculated easily)
so marked price = 1.3333*60 = 80
profit to be earned = 20%
final selling price = 1.2*60 = 72
therefore discount to be given = 8/80 = 10%
answer - C
The answer is: C | C |
mathematics | The length of a rectangle is three times of its width. If the length of the diagonal is 8√10 then find the perimeter of the rectangle. | [
"77 cm",
"88 cm",
"64 cm",
"11 cm",
"18 cm"
] | Let Breadth = x cm,
then, Length = 3x cm
x2+(3x)2=(810−−√)2=>10x2=640=>x=8
x2+(3x)2=(810)2=>10x2=640=>x=8
So, length = 24 cm and breadth = 8 cm
Perimeter = 2(l+b)
= 2(24+8) = 64 cm
Answer:C
The answer is: C | C |
mathematics | Find how many positive integers less than 10,000 are there such thatthe sum of the digits of the no. is divisible by 3? | [
"3468",
"2378",
"2875",
"3334",
"3579"
] | If sum of the digits is divisible by 3, the number is divisible by 3.
Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.
Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).
Count ... | D |
mathematics | In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way? | [
"5 sec",
"4 sec",
"3 sec",
"6 sec",
"1 sec"
] | T = 30/36 * 18/5 = 3 sec
Answer: C
The answer is: C | C |
mathematics | The sum of two consecutive number is 49. Which is the larger number? | [
"42",
"43",
"25",
"45",
"46"
] | Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=49
2x+1=49
2x=48
x=24
Therefore larger number is x+1=25
ANSWER:C
The answer is: C | C |
mathematics | In a room there are 11 people. Each person shook hands with every other person. How many hand shakes were there? | [
"52",
"53",
"54",
"55",
"56"
] | 11C2 = 55
The answer is D.
The answer is: D | D |
mathematics | Excluding stoppages, the speed of a bus is 70 km/hr and including stoppages, it is 40 km/hr. For how many minutes does the bus stop per hour? | [
"118 min",
"10 min",
"18 min",
"16 min",
"25 min"
] | Due to stoppages, it covers 30 km less.
Time taken to cover 30 km = 30/70 * 60
= 25 min.
Answer:E
The answer is: E | E |
mathematics | Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 74 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad? | [
"3",
"4",
"5",
"6",
"8"
] | Total Distance = 74 kms
Maxwell Speed = 4 kms/hr
Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.
Time taken = Total Distance / Relative Speed
Total Distance after Brad started = 70 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be ... | E |
mathematics | Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? | [
"2:3:4",
"2:3:8",
"2:3:0",
"2:3:1",
"2:3:9"
] | Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased sears are (140% of 5x), (150% of 7x) and (175% of 8x)
i.e., (140/100 * 5x), (150/100 * 7x) and (175/100 * 8x)
i.e., 7x, 21x/2 and 14x
Required ratio = 7x:21x/2:14x
= 14x : 21x : 28x = 2:3:4
Answer... | A |
mathematics | If the sum of 5 consecutive integers is y, which of the following must be true?
I. y is an even number
II. y is an odd number
III. y is a multiple of 5 | [
"I only",
"II only",
"III and II only",
"I and III",
"III only"
] | I. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 5p + 10 = 5 ... | E |
mathematics | In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital? | [
"11758",
"11756",
"11753",
"11750",
"11751"
] | 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer: D
The answer is: D | D |
mathematics | Area of four walls of a room is 99 m2. The length and breadth of the room are 7.5 m and 3.5m respectively. The height of the room is: | [
"2.5m",
"3.5m",
"1.5m",
"4.5m",
"5.5m"
] | 2(7.5+3.5)×h = 99
2(11)h = 99
22h = 99
h = 99/22 = 9/2 = 4.5 m
Answer is D.
The answer is: D | D |
mathematics | A fruit salad mixture consists of apples, peaches, and grapes. There are 2 times as many pounds of apples as grapes and 3 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 9 pounds per fruit, how many more pounds of apples than grapes does the mixture have? | [
"15",
"12",
"9",
"6",
"3"
] | A+P+G= 9*2
A=2G
P=3G
3G+2G+G= 9*2
G= 9*2/6= 3
A= 3*2=6
Difference = 6-3=3
'E' is the answer
The answer is: E | E |
mathematics | Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 7 miles per hour. If both Tom and Linda travel indefinitely, what is the positive diffe... | [
"60",
"56",
"84",
"90",
"108"
] | B is the answer....
D = TS where D=distance, T=Time and S=Speed
To travel half distance, (2+2T) = 7T ==> T = 2/5 ==> 24 minutes
To travel double distance, 2(2+2T) = 7T ==> 2 ==>80 minutes
Difference, 56 minutes
B
The answer is: B | B |
mathematics | Ravi's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Ravi's average score on the 5 tests to be 80? | [
"80",
"82",
"84",
"86",
"88"
] | E. 88
Ravi must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 averag... | E |
mathematics | Jolene entered an 14-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, ... | [
"$506.00",
"$726.24",
"$900.00",
"$920.24",
"$926.24"
] | If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.
Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second ti... | A |
mathematics | 5n + 2 > 12 and 7n - 12 < 44; n must be between which numbers? | [
"2 and 8",
"2 and 6",
"0 and 9",
"2 and 7",
"2 and 9"
] | 5n+2 > 12
5n > 10
n > 2
7n-12 < 44
7n < 56
n < 8
So n must be between 2 and 8
2 < n < 8
correct answer A
The answer is: A | A |
mathematics | A man rows his boat 78 km downstream and 56 km upstream, taking 4 hours each time. Find the speed of the stream? | [
"6",
"5",
"7",
"8",
"3"
] | Speed downstream = d/t = 78/(4) = 20 kmph
Speed upstream = d/t = 56/(4) = 14 kmph
The speed of the stream = (20 - 14)/2 = 3 kmph
Answer:E
The answer is: E | E |
mathematics | x varies inversely as square of y. Given that y = 2 for x = 1. The value of x for y = 6 will be equal to? | [
"1/6",
"1/3",
"1/0",
"1/9",
"1/5"
] | Given x = k/y2, where k is a constant.
Now, y = 2 and x = 1 gives k = 4.
x = 4/y2 => x = 4/62, when
y = 6 => x = 4/36 = 1/9.
Answer:D
The answer is: D | D |
mathematics | The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 2:4:6, the price of the cheapest item is? | [
"2379",
"2889",
"9288",
"9000",
"7500"
] | Let their prices be 3x, 5x and 7x.
Then, 2x + 4x + 6x = (15000 * 3) or x = 3750.
Cost of cheapest item = 2x = Rs. 7500.
Answer: E
The answer is: E | E |
mathematics | X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number. | [
"2 only",
"3 only",
"1 and 3 only",
"2 and 3 only",
"1, 2 and 3"
] | Using the properties for even and odd numbers along with positive and negatives,
1. (X + Y) is an odd number : even + odd is always a odd number, so eliminate 1
2. Y^(X + Y) is an integer. : an odd and positive number could be raised to power of either positive or negative, so not conclusive, eliminate 2
3. X^Y is a po... | B |
mathematics | In a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein ? | [
"10",
"48 wheelers",
"37",
"97",
"12"
] | 3X + 4y = 240
by substitute through options 48 is correct
Answer: B
The answer is: B | B |
mathematics | Which of the following can be a perimeter t of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100 | [
"I only",
"III only",
"II and III only",
"I, II, and III",
"Not I, II, or III"
] | Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: t>0.
Answer... | D |
mathematics | The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? | [
"s.4538",
"s.8154",
"s.4518",
"s.4530",
"s.4517"
] | Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 9 = Rs.8154
Answer: B
The answer is: B | B |
mathematics | What number should replace the question mark? 2, 16, 4, 14, 6, 12, ---? | [
"8",
"10",
"12",
"14",
"16"
] | Answer: A
2, 16, 4, 14, 6, 12, 8?
There are two alternate sequences: +2 and -2.
The answer is: A | A |
mathematics | Find the area of a cuboid of length 8cm , breadth 10 cm . and height 12cm. | [
"900 cm cube",
"910 cm cube",
"920 cm cube",
"930 cm cube",
"960 cm cube"
] | Area of a cuboid = lxbxh =8cm x 10cm x 12cm = 960 cm cube
answer :E
The answer is: E | E |
mathematics | Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B. | [
"2:1",
"1:2",
"1:1",
"4:3",
"5:6"
] | 5% of A% of B = 2/3 (6% of A + 8% of B)
5A/100 = 4B/100 = 2/3(6A/100 + 8B/100)
=>3A=4B
A/B=4/3
A:B=4:3
ANSWER D
The answer is: D | D |
mathematics | Which of the following does NOT have a decimal equivalent that is a terminating decimal? | [
"1/2^25",
"5^3/2^7",
"3^8/6^10",
"3^9/6^7",
"6^8/10^10"
] | For a fraction to have terminating decimal, it must either have only 2 and/or 5 in the denominator. All other values in the denominator leads to non terminating decimal values
Hence,
1. A has 2 in the denominator, Hence it is terminating
2. B is also terminating
3. 3^8/(6^10) can be written as 3^8/ (2^10 * 3^10) => 1/(... | C |
mathematics | At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.6 minutes per mile and then turn around and drive at 0.6 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm? | [
"a) 10",
"b) 11",
"c) 55/3",
"d) 13",
"e) 14"
] | 0.8 minutes --> 1 mile
1 minute --> 1/0.6 = 10/6 = 5/3 miles/minute
Distance covered in 40 minutes = 5/3 * 40 = 200/3 miles
Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)
Let x be the miles driven before turning
30 + x = 200/3 - x
2x =... | C |
mathematics | A water tank has three taps A, B and C. Tap A, when opened,can fill the water tank alone in 4 hours. Tap B, when opened, can fill the water tank alone in 6 hours and tap C, when opened, can empty the water tank alone in 3 hours. If taps A, B and C are opened simultaneously, how long will it take to fill the tank comple... | [
"10 hours",
"8 hours",
"18 hours",
"12 hours",
"None of these"
] | Required time to fill the tank
= 1 /(1/4+1/6)−1/3=1 /5/12−1/3=1 /1/12=12h
Answer D
The answer is: D | D |
mathematics | A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? | [
"7",
"9",
"8",
"4",
"5"
] | 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 8
Answer:C
The answer is: C | C |
mathematics | There are 9 person among whom 2 are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to? | [
"4!*2!",
"7!*2!",
"6!*2!",
"2!*1!",
"5!*1!"
] | Total number of ways = 6!*2!.
C
The answer is: C | C |
mathematics | In Town X, 60 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females? | [
"16%",
"20%",
"31%",
"40%",
"52%"
] | We are asked to find the percentage of females in employed people.
Total employed people 60%, out of which 48 are employed males,hence 12% are employed females.
(employed females)/(total employed people)=12/60=1/5=20%
Answer: B.
The answer is: B | B |
mathematics | 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed? | [
"6",
"7 2⁄3",
"6 2⁄3",
"6 1⁄3",
"None of these"
] | 10 men + 15 women in 1 day do 1⁄15 + 1⁄12 = 9⁄60 work
\ Time taken = 60⁄9 days = 62⁄3 days
Answer C
The answer is: C | C |
mathematics | For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 10, -3, 20, 5, -4, 6, -7 , 12? | [
"1",
"2",
"3",
"4",
"5"
] | The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.
10*(-3)=-30=negative;
-3*20=-60=negative;
5*(-4)=-20=negative.
6 * (-7) = -42 > negative
-7 * 12 = -84 >>negative
So there are 5 pairs of consecutive terms.
Answer: E... | E |
mathematics | The length of the bridge, which a train 150 metres long and travelling at 54 km/hr can cross in 30 seconds, is? | [
"340 m.",
"350 m.",
"320 m.",
"330 m.",
"360 m."
] | Speed = [54X 5/18] m/sec = [15] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 15 => (130 + x)/30
= 320 => x
= 320 m.
Answer:C
The answer is: C | C |
mathematics | Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 100 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? | [
"66",
"70",
"72",
"75",
"78"
] | Let the distance one way be x
Time from home to work = x/60
Time from work to home = x/100
Total time = 2 hrs
(x/60) + (x/100)= 2
Solving for x, we get x = 75
Time from home to work in minutes= (75)*60/60 = 75 minutes
Ans= D
The answer is: D | D |
mathematics | Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many straight lines can be formed by joining them ? | [
"124",
"144",
"134",
"142",
"143"
] | The number of straight lines formed joining the 18 points, taking 2 at a time = 18C2=153. Number of straight lines formed by joining the 5 points, taking 2 at a time =5C2=10. But 5 collinear point, when joined pairwise give only one line. Required number of straight lines =153-10+1 =144. Answer :B
The answer is: B | B |
mathematics | 3, 5, 7, 11, 13, 17, 19, ____ | [
"25",
"36",
"23",
"49",
"27"
] | The sequence is a series of prime numbers, 3, 5, 7, 11, 13, 17, 19, 23....
Answer : C.
The answer is: C | C |
mathematics | Find the average of all prime numbers between 1 and 10 | [
"2.5",
"1.35",
"4.25",
"6.12",
"7.13"
] | Prime numbers between 1 and 10 are 2,3,5,7
Required average = (2+3+5+7)/4 = 17/4 = 4.25
Answer is C
The answer is: C | C |
mathematics | A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 13.69, the number of the member is the group is: | [
"57",
"67",
"37",
"87",
"97"
] | Money collected =(13.69 x 100) paise = 1369 paise
numbers of members = 1369 squareroot = 37
Answer C
The answer is: C | C |
mathematics | P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 130 days, in how many days can R alone complete the remaining work? | [
"50 days",
"83.6 days",
"100 days",
"150 days",
"80 days"
] | P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days
Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days
P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and... | B |
mathematics | If 0.75: x :: 5:7, then x is equal to: | [
"1.05",
"1.16",
"1.2",
"1.3",
"None of these"
] | Explanation:
(x * 5) = (0.75 *7)
X=5.25/5 = 1.05
Answer: A
The answer is: A | A |
mathematics | A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed? | [
"1 hour 40 minutes",
"1 hour 38 minutes",
"1 hour 20 minutes",
"1 hour 44 minutes",
"2 hour 20 minutes"
] | Let the distance and original speed be d km and k kmph respectively.
d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3
=> (5d - 4d)/4k = 1/3 => d = 4/3 k
Time taken to cover the distance at original speed
= d/k = 4/3 hours = 1 hour 20 minutes.
Answer: C
The answer is: C | C |
mathematics | 2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have been was full he findsthe waste pipe open. He then closes the waste pipe and in another 4 mins the cistern was full. In what time can the waste pipe empty the cistern when fi... | [
"1/5",
"1/3",
"2/7",
"3/5",
"3/11"
] | 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
B
The answer is: B | B |
mathematics | The cricket team of 11members is 25yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ? | [
"21",
"22",
"23",
"25",
"28"
] | Let the average age of the whole team be x years.
11x - (25 + 28) = 9 (x - 1)
=> 11x - 9x = 44
=> 2x = 44
=> x = 22.
So, average age of the team is 22 years.
B
The answer is: B | B |
mathematics | A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives? | [
"14200",
"14700",
"14800",
"14500",
"None of these"
] | Explanation :
Total amount invested = 50000
Assume that investment of C = x.
Then investment of B = 5000 + x ,
Investment of A = 4000 + 5000 + x = 9000 + x
x + 5000+x + 9000 + x = 50000
=> 3x + 14000 = 50000
=> 3x = 50000 – 14000 = 36000
=> x = 36000/3 = 12000
=> Investment of C = x = 12000 ,
Investment of B = 5000 + x... | B |
mathematics | In a village of 2,600 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old? | [
"221/250",
"199/250",
"33/50",
"8/25",
"209/260"
] | The number of people younger than 70 years old is 2600-800 = 1800
The number of females older than 70 years old is 0.6*850 = 510
Then the number of males older than 70 years old is 800 - 510 = 290.
The number of people who are either male or younger than 70 is 1800+290 = 2090.
P(a person is younger than 70 or male) = 2... | E |
mathematics | Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 40 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly... | [
"3.625",
"3.5",
"3",
"3.04",
"4"
] | Set up two R x T =D cases.
1. 1/12 km/ min x T = 2.75
from which T= 33 mins.
We know total journey time now is 40 +33 =73.
The rate is the same ie 1/12km/min.
set up second R x T =D case.
1/12 km/min x 73 = 6.08 km
Now the total journey would be halved as distance would be same in each direction. 6.08/2 =3.04
D.
The an... | D |
mathematics | find S.P when CP=56.25,gain=20%. | [
"Rs 66.50",
"Rs 65.50",
"Rs 67.50",
"Rs 69.50",
"Rs 68.50"
] | SP =20% of Rs 56.25 ,=Rs{(120/100)*56.25}=Rs67.50
Answer is C
The answer is: C | C |
mathematics | If a is an odd integer and b is an odd integer which of the following must not be an odd integer : | [
"a/b",
"ab",
"2a+b",
"2(a+b)",
"3a/b"
] | only when two odd number added then we get even number.
Therefore answer is D
The answer is: D | D |
mathematics | A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 12m/h. what is the speedof the person while he was going to his office? | [
"8km/h",
"12km/h",
"14km/h",
"16km/h",
"17km/h"
] | u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=12
\inline \Rightarrow 1.5k = 12
\inline \Rightarrow k=8km/h
A
The answer is: A | A |
mathematics | Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/4 of the remaining paint. How many gallons of paint has Joe used? | [
"18",
"157",
"175",
"216",
"250"
] | Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/4)*270 = 67 gallons
Total paint used = 157 gallons.
Option B
The answer is: B | B |
mathematics | Notebooks are sold in packages of four or seven only. If Wilson bought 69 notebooks exactly, what could be the number of large packs Wilson bought? | [
"3",
"4",
"7",
"8",
"9"
] | Let number of packs of four = f
let number of packs of seven = s
4f + 7s = 69
Now , we need to test for values of s .
Since sum 69 is odd and 4f will always be even , e can't be even .
Now , we can test for values e = 3 , 7 and 9
4*5 + 7*7 = 20 + 49 = 69
Answer C
The answer is: C | C |
mathematics | If X-Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z? | [
"-4.5.",
"-2.",
"-1.7.",
"-0.667.",
"2.5."
] | X-Y = 2X-2Z
Y= -X+2Z---------- 1
X-2Y = 4Z
X-4Z= 2Y--------- 2
Adding equation 1 from equation 2
-2Z= 3Y
Y/Z= -0.667
D is the answer
The answer is: D | D |
mathematics | In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ? | [
"100",
"72",
"110",
"135",
"145"
] | Explanation :
Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x.
.'. 60% of x = 36 +5/6 *36
=>60/100 * x = 66
=>x = 110
Answer : C
The answer is: C | C |
mathematics | if india=90 and france=146 then england equals to? | [
"215",
"216",
"217",
"218",
"219"
] | I=9 N=14 D=4 I=9 A=1
(9*1)+(14*2)+(4*3)+(9*4)+(1*5) = 90
Multiply code of each lettr wid 1 2 3 in dat order...
Similarly france wil b
(6*1)+(18*2)+(1*3)+(14*4)+(3*5)+(5*6)= 146
In dat manner england will be 219
ANSWER:E
The answer is: E | E |
mathematics | A train running at the speed of 40 km/hr crosses a pole in 27 seconds. What is the length of the train? | [
"250",
"300",
"350",
"400",
"450"
] | Speed=(40 * 5/18) m/sec = (100/9) m/sec Length of the train = (Speed x Time) = (100/9 *29 ) m
= 300 m.
Answer: B
The answer is: B | B |
mathematics | What percent is 1 gm of 1 kg? | [
"0.1 %",
"1%",
"1.5%",
"2%",
"3%"
] | 1 kg = 1000 gm
1/1000 × 100 = 100/1000
=1/10 = 0.1 %
A)
The answer is: A | A |
mathematics | What is the ratio of the volumes of a right cylinder to that of a right cone having equal diameters? | [
"1:3",
"3:1",
"2:3",
"3:2",
"None of these"
] | SOLUTION :
volume of cylinder : volume of cone
pr2h : 1/3 pr2h = 3 : 1
ANSWER IS B
The answer is: B | B |
mathematics | Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank? | [
"8 min",
"28 min",
"18 min",
"5 min",
"6min"
] | Explanation :
Part filled by pipe A in 1 minute= 1/12
Part filled by pipe B in 1 minute= 1/24
Part filled by pipe A and pipe B in 1 minute= 1/12+1/24=1/8
i.e., both the pipe together can fill the tank in 8 minutes
Answer is A
The answer is: A | A |
mathematics | Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 25 seconds, what is the ratio of their speeds? | [
"1:3",
"4:1",
"2:3",
"3:2",
"3:4"
] | Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 25 s
= (27x + 17 y)/(x+y) = 25
= (27x + 17 y)/ = 25(x+y)
= 2x = 8y
=x/y = 8/2 = 4/1 i.e 4:1
Answer :B
The answer is: B | B |
mathematics | Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 100% more than Bert had in savings, and separately, the same price was also 60% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings. | [
"1:5",
"2:5",
"3:5",
"4:5",
"1:1"
] | Suppose bert had 100 so price becomes 200 , this 200 = 1.6 times R's saving .. so R's saving becomes 125
So required ratio is 100:125=4:5
ANSWER:D
The answer is: D | D |
mathematics | A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 5 days. B can do the work alone in? | [
"19",
"12",
"11",
"30",
"114"
] | Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/5
6/x = 1/5 => x = 30
So, B takes 15 hours to finish the work.
Answer: D
The answer is: D | D |
mathematics | Find a sum for first 8 prime numbers? | [
"22",
"28",
"59",
"77",
"84"
] | Required sum = (2 + 3 + 5 + 7 + 11+13+17+19) = 77
Note: 1 is not a prime number
Option D
The answer is: D | D |
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