subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | 7 liters of a 22 percent solution of alcohol in water are mixed with 3 liters of an 11 percent alcohol in water solution. What is the percentage of alcohol in the new solution? | [
"17.5%",
"17.8%",
"18.1%",
"18.4%",
"18.7%"
] | The total amount of alcohol is 0.22(7) + 0.11(3) = 1.87 liters.
The percentage is 1.87 / 10 = 18.7 / 100 which is 18.7%
The answer is E.
The answer is: E | E |
mathematics | The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son | [
"34,11",
"35,10",
"36,9",
"40,5",
"41,5"
] | Explanation:
Let sons age = x years. Then fathers age = (45 - x)years.
(x—5)(45—x—5) = 4(45- x - 5) hence (x—5) = 4 so x = 9
Their ages are 36 years and 9 years.
Answer: Option C
The answer is: C | C |
mathematics | If x > 0, x/40 + x/20 is what percent of x? | [
"6%",
"25%",
"37 1/2%",
"60%",
"75 %"
] | Just plug and chug. Since the question asks for percents, pick 100. (but any number will do.)
100/40 + 100/20= 2.5+5=7.5
7.5 is 75% of 100=E
The answer is: E | E |
mathematics | A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at? | [
"12 min",
"16 min",
"18 min",
"15 min",
"19 min"
] | Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 6 - 1 = 5 rounds per hour.
Time taken to complete one round at this speed
= 1/5 hr
= 12 min.
Answer:A
The answer is: A | A |
mathematics | The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 25 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B? | [
"75%",
"25%",
"10%",
"45%",
"180%"
] | Let length of each side of square A be 10
Area of A = 10^2 = 100
Since , length of each side of square A is increased by 100 percent to make square B
length of each side of square B = 2*10 = 20
Area of B = 20^2 = 400
Since , length of the side of square B is increased by 25 percent to make square C
length of each side ... | D |
mathematics | For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 7, 8, 8, 7, 9, 9, 6, 7, 8 and 7. By what percent did she fall short of her goal? | [
"4%",
"5%",
"8%",
"10%",
"12%"
] | Expected minimum rating = 8
Deviation from the expected minimum rating = (-1 + 0 + 0 - 1 + 1 + 1 - 2 - 1 + 0 - 1)/10 = -4/10 = -0.4
Current rating is 0.4 less than 8.
Percentage = (0.4/8)*100 = 5%
Answer: B
The answer is: B | B |
mathematics | find value for x from below equation? x + 1 = 5 | [
"-5",
"-4",
"4",
"3",
"2"
] | 1. Subtract 1 from both sides:
x + 1 - 1 = 5 - 1
2. Simplify both sides:
x = 4
C
The answer is: C | C |
mathematics | Pradip spends 40 per cent of his monthly income on food items, and 50 per cent of the remaining on clothes and conveyance. He saves one-third of the remaining amount after spending on food, clothes and conveyance. If he saves 19,200 every year,what is his monthly income? | [
"24,000",
"12,000",
"16,000",
"20,000",
"None of these"
] | Food items = 40%
Clothes + conveyance = 1⁄2 of 60% = 30%
1⁄3 of 30% = 19,200⁄12 ⇒ 10% = 1600
∴ 100% = 16,000
Answer C
The answer is: C | C |
mathematics | To make 552185 divisible by 8, what is the least whole number that should be added to it? | [
"3",
"7",
"9",
"6",
"4"
] | A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
Here, 552185=185(no formed by last three digit)
the next multiple of 8 is 192
7 must be added to 552185 to make it divisible by 8
B
The answer is: B | B |
mathematics | 64, 81, 100, 144, 196, ?, F ind the missing number(?). | [
"225",
"220",
"230",
"238",
"278"
] | The series consists of squares of consecutive composite numbers.
Answer : A.
The answer is: A | A |
mathematics | A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent? | [
"11",
"25",
"66",
"88",
"11"
] | 600 --- 400
100 --- ? => 66%
Answer:C
The answer is: C | C |
mathematics | 27 * 27* 27 * 27 = 3^ ? | [
"7",
"12",
"5",
"6",
"8"
] | 3^3 * 3^3 * 3^3 * 3^3 = 3^ (3+3+3+3) = 3^12
Answer : 12
Option : B
The answer is: B | B |
mathematics | A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 14km? | [
"3",
"6",
"8",
"9",
"7"
] | M = 4
S = 2
US = 4 - 2 = 2
D = 14
T = 14/2 = 7
Answer:E
The answer is: E | E |
mathematics | There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? | [
"320",
"345",
"375",
"380",
"400"
] | In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence
3x + 5x = 600
Solve for x
8x = 600
x = 75
Number of boys
3x = 3 ... | C |
mathematics | A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? | [
"37",
"240",
"288",
"267",
"211"
] | Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: B
The answer is: B | B |
mathematics | Arun's Ice Cream Shop sells ice cream at x cents a scoop. For an additional y cents, a customer can add 4 toppings to his or her sundae. How much would a sundae with 4 scoops and 4 toppings cost, in terms of x and y? | [
"3x+y",
"5x+y",
"6x+y",
"4x+y",
"7x+y"
] | Answer A 4x+y
The answer is: A | A |
mathematics | A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability E of generating an odd prime digit is between | [
"0 and 1/6",
"1/6 and 1/3",
"1/3 and 1/2",
"1/2 and 2/3",
"2/3 and 5/6"
] | K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1
Note that 1/10 is least value and is equal to 0.1 so we can write above series as
K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1
K=1/3+
P (3 or 5 or 7) =K*13/24
Required probability E= 13/24 × 1/3+ = 4+/24 > 1/6
Answer should be B
P.s. 3+ denotes a value litt... | B |
mathematics | 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? | [
"20",
"10",
"30",
"40",
"50"
] | C
30
3W = 2M
15M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
15 * 21 * 8 = 14 * x * 6
x = 30
The answer is: C | C |
mathematics | If the sum of three consecutive even numbers is 44 more than the average of these numbers, then the largest of these numbers is? | [
"20",
"24",
"22",
"26",
"27"
] | Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 44
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 132
9x + 18 = 3x + 138
6x = 120
x = 20
Therefore, the largest number is 24.
ANSWER B
The answer is: B | B |
mathematics | The length of the bridge, which a train 130 metres long and travelling at 54 km/hr can cross in 30 seconds, is: | [
"200 m",
"225 m",
"320 m",
"250 m",
"240 m"
] | Speed = [54 X 5/18] m/sec = [15/1] m/sec
Time = 30 sec
Let the length of bridge be x metres.
Then, (130 + x)/30 = 15 => (130 + x) = 450 => x = 450-130 = 320m
ANSWER:C
The answer is: C | C |
mathematics | Simple interest on a certain amount is 9/16 of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is : | [
"6 1/2",
"7 1/2",
"8",
"9 1/2",
"None"
] | Sol.
Let sum = x. Then, S.I. = 9/16 x.
Let rate = R% and time = R years.
∴ [x * R * R / 100] = 9x / 16 ⇔ R² = 900/16
⇔ R = 30/4 = 7 1/2
Hence, time = 7 1/2 years.
Answer B
The answer is: B | B |
mathematics | How many two-digit numbers yield a remainder of 3 when divided by both 4 and 14? | [
"0",
"1",
"2",
"3",
"4"
] | Easier to start with numbers that are of the form 14p+3 ---> 17,31,45,59,73,87.
Out of these 3 (31,59,87) are also of the form 4q+3. Thus 3 is the answer. D is the correct answer.
The answer is: D | D |
mathematics | In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground? | [
"70",
"52",
"62",
"59",
"50"
] | total number of players= 16+12+18+13= 59
Answer is D
The answer is: D | D |
mathematics | If a number is subtracted from its square we get 272. Find the number? | [
"7",
"21",
"19",
"15",
"17"
] | x^2 – x = 272
=> x =17
Answer E
The answer is: E | E |
mathematics | A positive number x is multiplied by 4, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ? | [
"9/4",
"3/2",
"4/3",
"1/3",
"1/2"
] | We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:
2x/3
Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us
√(2x/3) = x
2x/3 = x^2
2x = 3x^... | D |
mathematics | A firm has 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different) | [
"48",
"100",
"120",
"288",
"600"
] | Total no of groups of 3 members (including junior and senior) = 10C3
Total no of groups of 3 members (only juniors) = 6C3
Total no of groups of 3 members (at least 1 senior) = 10C3 - 6C3 = 120 - 20 =100
ans:B
The answer is: B | B |
mathematics | By investing in 16 % stock at 64, one earns Rs. 1500. The investment made is: | [
"5760",
"7667",
"4445",
"4566",
"3344"
] | Explanation:
To earn Rs., investment = Rs. 64.
To earn Rs. 1500, investment = = Rs. 5760.
Answer: C) 5760
The answer is: C | C |
mathematics | If x and y are positive integers such that y is a multiple of 5 and 3x + 8y = 700, then x must be a multiple of which of the following? | [
"3.",
"6.",
"7.",
"8.",
"10."
] | If y is a multiple of 5, then 8y is also a multiple of 5.
3x = 700 - 8y
700 - 8y is even and it is a multiple of 5.
Thus x must also be even and a multiple of 5.
Therefore x must be a multiple of 10.
The answer is E.
The answer is: E | E |
mathematics | The average of first 50 non-zero positive integers is | [
"11.5",
"25.5",
"22",
"25",
"27"
] | Explanation :
Sum of first n non-zero positive integers n(n + 1)/2
So, average of first n non-zero positive integers n(n + 1)/2n = (n + 1)/2
=> (50 + 1)/2 = 25.5
Answer : B
The answer is: B | B |
mathematics | A woman has four blouses of different colors, three skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear? | [
"8",
"22",
"16",
"17",
"18"
] | total ways = 4*3*2=24..
now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..
the ways in which the pink blose and green skirty are together=1*1*2=2..
total ways =24-2=22..
B
The answer is: B | B |
mathematics | 18% of 680 - ? = 68.7 | [
"44.1",
"32.4",
"66.5",
"75.2",
"53.7"
] | E
53.7
(18 *680)/100 - ? = 68.7
? = 122.4 - 68.7
? = 53.7
The answer is: E | E |
mathematics | Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? | [
"1/2",
"3/8",
"3/4",
"5/16",
"9/16"
] | In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(E) = 27.
P(E) = n(E)/n(S)... | C |
mathematics | A train 700 m long passes a man, running at 20 km/hr in the same direction in which the train is going, in 40 sec. The speed of the train is? | [
"40 km/hr",
"41 km/hr",
"42 km/hr",
"43 km/hr",
"44 km/hr"
] | Speed of the train relative to man = 700/40 = 35/2 m/sec.
= 35/2 * 18/5 = 63 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 20) km/hr.
x - 20 = 63 => x = 43 km/hr.
Answer: D
The answer is: D | D |
mathematics | If 3 men or 4 women can reap a field in 43 days how long will 7 men and 5 women take to reap it? | [
"9",
"12",
"15",
"18",
"19"
] | Explanation:
3 men reap 1/43 field in 1 day
1 man reap 1/(3 x 43)
4 women reap 1/43 field in 1 day
1 woman reap 1/(43 x 4)
7 men and 5 women reap (7/(3 x 43)+ 5/(4 x 43)) =1/12 in 1 day
7 men and 5 women will reap the field in 12 days
Answer: Option B
The answer is: B | B |
mathematics | in a certain flower shop, which stocks four types of flowers, there are 1/4 as many violets as carnations, and 1/4 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations? | [
"31",
"30",
"29",
"28",
"27.27"
] | Given :-
Violets - C/4
Carnations - C
Tulip - C/16
Rose - C/16
Total flowers in terms of C = C/4+C+C/16+C/16 = 22C/6
Percentage of Carnations = C/22C/6 *100 =27.27
Answer E
The answer is: E | E |
mathematics | If I walk at 8 km/h, I miss the bus by 14 minutes. If I walk at 9 km/h, I reach 16 minutes before the arrival of the bus. How far I walk to reach the bus stand ? | [
"3.4 km",
"2.9 km",
"2.4 km",
"2.6 km",
"2.8 km"
] | d = product of speed difference of time /difference of speed
d = 8 X 9/60[14−(−16)/9-8]
[Here, –ve sign indicates before the schedule time]
⇒ d = 2.4 km
Answer C
The answer is: C | C |
mathematics | what is next no. 11 23 47 83 131 191 263 347 443 551??? | [
"171",
"181",
"191",
"201",
"671"
] | 11+12*1=23
23+12*2=47
47+12*3=83
83+12*4=131
131+12*5=191
191+ 12*6=263
263+12*7=347
347+12*8=443
443+12*9=551
551+12*10=671
ANSWER:E
The answer is: E | E |
mathematics | A certain debt will be paid in 65 installments from January 1 to December 31 of a certain year. Each of the first 20 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 20 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year? | [
"443",
"455",
"465",
"468",
"475"
] | Total number of installments = 65
Payment per installment for the first 20 installments = 410
Payment per installment for the remaining 45 installments = 410+65=475
Average = (20*410 + 45*475)/65 = 455
Answer B
The answer is: B | B |
mathematics | In a party every person shakes hands with every other person. If there were a total of 171 handshakes in the party then what is the number of persons present in the party ? | [
"15",
"16",
"17",
"18",
"19"
] | Explanation :
Let the number of persons be n
∴ total handshakes = nC2 = 171
n(n-1)/2 = 171 ∴ n = 19
Answer : Option E
The answer is: E | E |
mathematics | Express a speed of 16 kmph in meters per second? | [
"10 mps",
"8 mps",
"4 mps",
"7 mps",
"2 mps"
] | 16 * 5/18
= 4 mps
Answer:C
The answer is: C | C |
mathematics | The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle? | [
"2&4",
"3&5",
"4&6",
"5&7",
"6&8"
] | Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations.
15 = x y and 16 = 2 x + 2 y
Solve the second equation for x
x = 8 - y
Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as
15 = (8 - y) y
Solve for y to find
y = 3 an... | B |
mathematics | What is the radius of the circum circle of the triangle whose sides are 5, 12 and 13 units respectively? | [
"2 units",
"12 units",
"6.5 units",
"6 units",
"7.5 units"
] | sides of triangle are 5,12,13
i.e triangle is right angled,hypotenuse=13
in case of a right angled triangle, the hypotenuse is the diameter of the circumcircle
so radius of the circum circle=13/2=6.5 units
ANSWER:C
The answer is: C | C |
mathematics | A train covers a distance of 12 km in 10 min. If it takes 4 sec to pass a telegraph post, then the length of the train is? | [
"20",
"110",
"120",
"80",
"60"
] | Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 4= 80 m.
Answer: Option D
The answer is: D | D |
mathematics | If P is a prime number greater than 5, what is the remainder when P^2 is divided by 8. | [
"4",
"3",
"2",
"1",
"Cannot be determined"
] | Here is the algebraic approach..
these prime numbers are of teh form 6n+1 or 6n-1..
so P= 6n+1..
P^2=(6n+1)2=36n^2+12n+1
Now 36n^2+12n=4n(9n+3)
if n is even... 4n will be div by 8....
if n is odd.. 4n will be div by 4 and 9n+3 will become even and be div by 2,hence 4n*(9n+3) will be div by 4*2=8..
so in P^2=36n^2+12n+1... | D |
mathematics | A company D has 15 percent of the employees are secretaries and 10 percent are salespeople. If there are 120 other employees of Company D, how many employees does Company D have? | [
"200",
"160",
"180",
"152",
"250"
] | Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 10%
% of of employees other than secretaries and salespeople = 100 - 25 = 75%
But this number is given as 120
so 75% of x = 120
x = 160
Therefore there a total of 160 employees in the company D
Correct answer - B
The answer ... | B |
mathematics | 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds | [
"11:9",
"13:9",
"17:9",
"21:9",
"None of these"
] | Explanation:
We know total distance is 200 Km
If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110+90=200km]
So ratio of their speed = 110:90 = 11:9
Option A
The answer is: A | A |
mathematics | If 15% of 40 is greater than 25% of a number by 2, the number is | [
"14",
"16",
"18",
"20",
"22"
] | Explanation:
15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16
Option B
The answer is: B | B |
mathematics | Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work? | [
"22 days",
"68 days",
"77 days",
"11 days",
"88 days"
] | (5 + x)/20 + 5/25 = 1 => x = 11 days
Answer: D
The answer is: D | D |
mathematics | A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement? | [
"1900",
"2776",
"8888",
"1666",
"1878"
] | 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer: A
The answer is: A | A |
mathematics | If the equation x^2−6x=2k has at least one solution, which of the following must be true? | [
"k > 9",
"k < −9",
"k = 9",
"k ≤ 9",
"k ≥ −9/2"
] | x^2−6x=2k
=> x^2−6x - 2k = 0
For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.
b^2-4ac ≥0
=> 36 - 4*1*(-2k) ≥0
=> 36 + 8k ≥0
=> k ≥ -9/2
Answer E
The answer is: E | E |
mathematics | A group of students was interviewed for that if it was asked whether or not they speak French and / or English. Among those who speak French, 10 speak English well, while 40 of them do not speak English. If 75% of students do not speak French, how many students were surveyed? | [
"210",
"225",
"200",
"250",
"300"
] | Number of students who speak French are 40 + 10 = 50
Of total students, the percentage of students who do not speak French was 75% --> percentage of who do is 25%
50-------25%
x ------- 100%
x = 50*100/25 = 200 = number of all students
Answer is C
The answer is: C | C |
mathematics | What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years? | [
"5",
"6",
"7",
"8",
"9"
] | 160 = (180*4*R)/100
R = 5%.Answer: A
The answer is: A | A |
mathematics | If an object travels at nine feet per second, how many feet does it travel in one hour? | [
"30",
"300",
"720",
"1800",
"32400"
] | Speed = 9 feet per second.
1 Hour= 60X60 Seconds = 3600 Seconds.
Total no of feet traveled in 1 hour = 3600X9 = 32400
Answer E
The answer is: E | E |
mathematics | A bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind? | [
"337",
"268",
"144",
"772",
"997"
] | Let the number of coins of each kind be x.
=> 5x + 2x + 1x = 1152
=> 8x = 1152 => x = 144
Answer:C
The answer is: C | C |
mathematics | Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ? | [
"5/16",
"5/12",
"5/87",
"5/56",
"5/38"
] | Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer:B
The answer is: B | B |
mathematics | In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 270 tiles in the floor, how many tiles does the leftmost row contain? | [
"38",
"56",
"60",
"64",
"68"
] | This question can be solved in a variety of ways: with algebra, by TESTing THE ANSWERS and by using a great Number Property shortcut involving consecutive integers.
We're given a few facts to work with:
1) There are 9 rows of tiles.
2) When going from 'left to right', each row contains TWO FEWER tiles than the one next... | A |
mathematics | A ship sails out to a mark at the rate of 18 kmph. and sails back at the rate of 14 kmph. The average rate of sailing is ? | [
"5 km/hr",
"12 km/hr",
"16 km/hr",
"25 km/hr",
"None"
] | Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 18 x 14 ) / (18 +14 ) km/hr.
= 16 km/hr.
Correct Option: C
The answer is: C | C |
mathematics | A, Band C can do a piece of work in 35 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days? | [
"7 days",
"8 days",
"9 days",
"10 days",
"16 days"
] | (A+B)'s 1 day's work = 1/35+1/20 = 11/140
(A+C)'s 1 day's work = 1/35+1/55 = 18/385
work done in 2 day's = 11/140+18/385 = 48/383
48/383th work done in 2 days
work done= 383/48*2 = 16 days (approx)
ANSWER:E
The answer is: E | E |
mathematics | A train 220 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? | [
"12",
"6",
"7",
"8",
"9"
] | Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 220 * 3/55 = 12 sec.
Answer: Option A
The answer is: A | A |
mathematics | How many even multiples of 45 are there between 449 and 901? | [
"5",
"6",
"9",
"10",
"11"
] | 450 = 10*45
900 = 20*45
The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B.
The answer is: B | B |
mathematics | For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [5]*[6] equivalent to? | [
"[45]",
"[30]",
"[15]",
"[5]",
"[50]"
] | [5]*[6] = 15*3 = 45 = [15]
The answer is C.
The answer is: C | C |
mathematics | A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey? | [
"19 kmph",
"24 kmph",
"17 kmph",
"12 kmph",
"16 kmph"
] | Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.
Answer:B
The answer is: B | B |
mathematics | For an upcoming charity event, a male vocalist has agreed to sing 7 out of 9 “old songs” and 5 out of 8 “new songs.” How many ways can the singer make his selection? | [
"25",
"50",
"150",
"480",
"161.28"
] | =9C7*8C5
=9*8/5*8*7/5
=161.28
Ans = E
The answer is: E | E |
mathematics | How many shots of 1cm radius can be prepared from a sphere of 2cm radius? | [
"3",
"8",
"27",
"88",
"99"
] | 4/3 π * 2 * 2 * 2 = 4/3 π * 1 * 1 * 1 * x
x = 8
Answer: B
The answer is: B | B |
mathematics | what is the remainder when 789456123 is divided by 999 | [
"349",
"359",
"369",
"379",
"389"
] | there is a simple trick for 99 or 999..u have to add the digits from right side for 99 you will select the last 2 digits and add with next two last digits and go on..similarly for 999 u will add last three digits then its next two last digits and so on..
so you will get 123 + 456 +789 =1368 again select last 3 and add ... | C |
mathematics | Two numbers are in the ratio 3 : 4. If their L.C.M. is 84. what is sum of the numbers? | [
"49",
"56",
"76",
"84",
"85"
] | Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 84
=> 12x =84
=> x = 84/12 = 7
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 7 = 49
Answer: Option A
The answer is: A | A |
mathematics | What is the speed of the train in km/hr whose length is 360 metres which passes a pole in 18 seconds? | [
"59/9 km/hr",
"50/9 km/hr",
"25/6 km/hr",
"55/18 km/hr",
"60/18 km/hr"
] | Speed=(18x5/18)=5 m/sec.
Length of the train= 360 metre
Time=18s
Speed=length / time
Speed=(360/8)=20 m/sec = 20*5/18 km/hr = 50/9 km/hr
Answer: B
The answer is: B | B |
mathematics | The average of first 40 prime numbers is? | [
"15.41",
"16.41",
"15.61",
"15",
"16.91"
] | Explanation:
Average = (2+3+5+7+11+13+17+19+23+29+31+37)/12= 197/12= 16.41(Approx)
Answer is B
The answer is: B | B |
mathematics | Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively | [
"19",
"17",
"13",
"9",
"18"
] | Explanation:
Answer will be HCF of (28-10, 128-2, 147-3)
HCF of (18, 126, 144) = 18
Option E
The answer is: E | E |
mathematics | 6x − 12 = 6y
5y + 5x = 10
Which of the following is the number of solutions to the system of equations shown above? | [
"More than three",
"Exactly three",
"Exactly two",
"Exactly one",
"None"
] | 6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1
5y + 5x = 10
=>x + y = 2 -- 2
From equation 1 and 2 , we get
2x = 4
=> x=2
y=0
Therefore , the given system will have Exactly one solution
D
The answer is: D | D |
mathematics | 80% of the students of a village is 1600. The total students of the school is? | [
"2000",
"2500",
"3000",
"1800",
"2200"
] | X * (80/100) = 1600
X = 20 * 100
X = 2000
Answer: A
The answer is: A | A |
mathematics | The sum of ages of 5 children born at theintervals of 3 years each is 50 years. what is the age of the youngest child? | [
"4",
"5",
"9",
"8",
"10"
] | the age of children x, (x+3), (x+6) , (x+9) and (x+12) years.
x+(x+3)+(x+6)+(x+9)+(x+12)= 50
5x= 20 , x=4. correct answer (A)
The answer is: A | A |
mathematics | Suresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow? | [
"Rs.8500",
"Rs.6000",
"Rs.8000",
"Rs.9000",
"Rs.7000"
] | using the formula S.I=P*T*R/100
(x*6*3/100)+(x*9*5/100)+(x*13*3/100)=8160
x=8000
i.e money borrowed is Rs.8000
ANSWER:C
The answer is: C | C |
mathematics | A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used | [
"12 months",
"10 months",
"14 months",
"16 months",
"None of these"
] | Explanation :
B received 2/3 of the profit
=> A : B = 1 : 2
Let the total capital = x
Then A's capital = x/4
B's capital = x – x/4 = 3x/4
Assume B's money was used for b months
Then A:B = (x/4)*15 : (3x/4)*b = 1 : 2
=> 15/4 : 3b/4 = 1 : 2
=> 15 : 3b = 1 : 2
=> 5 : b = 1 : 2
=> 5/b = 1/ 2
=> b = 5*2 = 10. Answer : Optio... | B |
mathematics | How many numbers of 5 digits can be formed with the digits 0, 1, 2, 3, 4, 6 & 8 with no digit being repeated in the same number? | [
"2170",
"2160",
"4396",
"4500",
"3500"
] | As we have 5 digits.. and having no repeation..
For the first digit can't be "0".. so, possibilities are 6..
for the second digit the possibilities are 6 including "0" also..
for the third digit there are 5 possibilities
for the fourth digit 4 possibilities
for the fifth digit 3 possibilities..
so, total no.of numbers ... | B |
mathematics | Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for s... | [
"38",
"31",
"41",
"None of these",
"Cannot be determined"
] | Explanation :
Let there be x mints originally in the bowl.
Sita took 1/3 but returned 4. So, noe the bowl haa (2x/3) + 4 mints
Fatima took 1/4 of the remainder but returned 3. So, the bawl now has (3/4)((2x/3) + 4) + 3 mints.
Eshwari took half of the remainder that is (1/2) [ (3/4) ( (2x/3) + 4 ) + 3 ]
She returns 2, s... | 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. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? | [
"4338",
"4536",
"4538",
"4530",
"4531"
] | 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 * 5 = Rs. 4530
Answer: D
The answer is: D | D |
mathematics | The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child? | [
"7 years",
"9 years",
"6 years",
"4 years",
"5 years"
] | 28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer: D
The answer is: D | D |
mathematics | A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 343, what was his profit? | [
"s. 63",
"s. 69",
"s.72",
"s.75",
"s.90"
] | C.P. = Rs. (100/122.5)x343
= Rs. (1000/1225)x343
= Rs. 280
Profit = Rs. (343 - 280) = Rs. 63.
Answer:A
The answer is: A | A |
mathematics | Find the smallest number which when divided by 13 and 17 leaves respective remainders of 3 and 7. | [
"187",
"211",
"207",
"219",
"227"
] | Let 'N' is the smallest number which divided by 13 and 17 leaves respective remainders of 3 and 7.
Required number = (LCM of 13 and 17) - (common difference of divisors and remainders) = (221) - (10) = 211.
ANSWER:B
The answer is: B | B |
mathematics | A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is? | [
"20",
"25",
"27",
"22",
"91"
] | Let the son's present age be x years.
Then, man's present age = (x + 22) years.
(x + 22) + 2 = 2(x + 2) x + 24 = 2x + 4 => x = 20.
Answer: A
The answer is: A | A |
mathematics | In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole? | [
"27",
"29",
"17",
"10",
"86"
] | Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
Answer:D
The answer is: D | D |
mathematics | In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together? | [
"1242",
"1728",
"1484",
"1734",
"1726"
] | Soln:
= 3! * 4! * 2! * 3!
= 1728
Ans is B
The answer is: B | B |
mathematics | A runs twice as fast as B and gives B a start of 64m.How long should the racecourse be so that A and B might reach in the same time? | [
"75 m.",
"128 m.",
"150 m.",
"100 m.",
"None of the above"
] | ratio of speeds of a and b is 2:1
b is 64m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 64m is 64/1=64m
so the total time taken by a and b to reach =2*64=128m
ANSWER:B
The answer is: B | B |
mathematics | A bat is bought for Rs.440 and sold at a gain of 20% find its selling price | [
"s.430/-",
"s.480/-",
"s.400/-",
"s.528/-",
"s.600/-"
] | 100 % ------> 440
120 % ------> 440*120/100
Selling price = Rs.528/-
D
The answer is: D | D |
mathematics | How many 4 digit number contain number 2 ? | [
"3168",
"3268",
"3368",
"3468",
"3568"
] | total 4 digit no. = 9*10*10*10 = 9000
not containing 2 = 8*9*9*9 = 5832
total 4 digit number contain 2 = 9000 - 5832 = 3168
ANSWER:A
The answer is: A | A |
mathematics | 6x − 24 = 6y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above? | [
"Exactly one",
"Exactly three",
"Exactly two",
"More than three",
"None"
] | 6x − 24 = 6y
=> 6x - 6y = 24
=> x- y =4 -- 1
5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 7
=> x=3.5
y=.5
Therefore , the given system will have Exactly one solution
Answer : A
The answer is: A | A |
mathematics | A bike covers a certain distance at the speed of 62km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel? | [
"85 km/h",
"82.66 km/h",
"87.67 km/h",
"90.25 km/h",
"90.64 km/h"
] | Ans.(B)
Sol. Total distance = 62 × 8 = 496 km
Now speed = 496/6 = 82.66 km/h
The answer is: B | B |
mathematics | A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 64 books in the special col... | [
"20",
"30",
"35",
"40",
"55"
] | there are 11 books less(75-64) which represents 20% of the loaned books (100-80)
So total loaned out books = 55
Answer E
The answer is: E | E |
mathematics | Beth received 2/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 2/3 of the votes cast? | [
"1/5",
"2/7",
"3/10",
"7/20",
"4/9"
] | Let the total votes be 100. Beth received 40 votes, other votes 100-40=60. In order to have received 1/2 of the votes she needed 200/3 votes so 80/3 more, which is 4/9 of the other votes.
Answer: E.
The answer is: E | E |
mathematics | Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is? | [
"8 days",
"12 days",
"14 days",
"16 days",
"18 days"
] | 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 = 10 × 40/50 = 8 days
A)
The answer is: A | A |
mathematics | Ramu bought an old car for Rs. 45000. He spent Rs. 12000 on repairs and sold it for Rs. 80000. What is his profit percent? | [
"16%",
"17%",
"40%",
"58%",
"13%"
] | Total CP = Rs. 45000 + Rs. 12000
= Rs. 57000 and SP = Rs. 80000
Profit(%)
= (80000 - 57000)/57000 * 100
= 40%
Answer: C
The answer is: C | C |
mathematics | There is a 20% chance that Lions will not win at all during the whole season. There is a 20% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Lions will win and Federer will play during the season? | [
"A)55%",
"B)60%",
"C)70%",
"D)72%",
"E)80%"
] | There is a 20% chance that Lions will not win at all during the whole season
We can infer that there is 80% chance Lions will win .
Similarly There is a 20% chance that Federer will not play at all in the whole season
We can also infer that there is 80% chance that Federer will play.
Answer E
The answer is: E | E |
mathematics | Two pipes P and Q can fill a cistern in 12 and 14 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? | [
"11 1/2 min",
"11 1/4 min",
"11 2/4 min",
"11 1/5 min",
"10 1/2 min"
] | 3/12 + x/14 = 1
x= 10 1/2
Answer: E
The answer is: E | E |
mathematics | A straight fence is to be constructed from posts 9 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot) | [
"17",
"28",
"35",
"39",
"40"
] | The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}
The minimum length is with 2 posts = 0.5 + 5 + 0.5 = 6 feet. To increase the fence, each time we should add{post = 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:
9 feet;
... | E |
mathematics | Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly? | [
"2661",
"1651",
"1267",
"1627",
"1261"
] | Explanation:
A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer:E
The answer is: E | E |
mathematics | A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $3.50, what total number of pens and pencils did the customer purchase? | [
"8",
"9",
"10",
"11",
"12"
] | Answer: Algebraically, the question looks like this: 2.5 = 0.35x + 0.25y There are six possible numbers of pens that fit that requirement:
1 pen: $0.35
2 pens: $0.70
3 pens: $1.05
4 pens: $1.40
5 pens: $1.75 balance can fetch 7 pencils for $0.25 each. That's 5 pens and 7 pencils for a total of 12 pens and pencils. Choi... | E |
mathematics | Pipe A can fill a tank in 7 hours, pipe B in 14 hours and pipe C in 42 hours. If all the pipes are open,in how many hours will the tank be filled ? | [
"4",
"4.2",
"4.5",
"4.3",
"4.1"
] | 1/7+1/14+1/42=10/42=1/4.2. so 4.2 hrs
ANSWER:B
The answer is: B | B |
mathematics | The arithmetic mean and standard deviation of a certain normal distribution are 17.5 and 2.5, respectively. What value is exactly 2 standard deviations less than the mean? | [
"10.5",
"11",
"11.5",
"12",
"12.5"
] | Mean = 17.5
Two standard deviations is 2.5 + 2.5 = 5.0
There could be two calues for this.
Mean + two standard deviations = 22.5
Mean - Two standard deviations = 12.5
Answer choice has 12.5 and so E is the answer.
The answer is: E | E |
mathematics | Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all | [
"15.5",
"15",
"16",
"Cant be computed",
"17"
] | Explanation:
As number of girls and boys is not given so result cant be computed
Answer: Option D
The answer is: D | D |
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