subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers W are possible? | [
"2",
"4",
"6",
"3",
"Not possible"
] | Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*... | C |
mathematics | A person has uncovered a secret that was a mystery for ages. He transfers the data into his hard drive and encrypts the drive with a password. Then, he writes a line on a paper to remember the password.
The line says 'You force heaven to be empty'.
Can you decrypt the line to reveal the password if you know that the pa... | [
"M472BMT",
"U472BMT",
"S472BMT",
"D472BMT",
"V472BMT"
] | B
The password is U472BMT.
Read aloud the line and you will sound something like "U Four Seven 2 B M T".
The answer is: B | B |
mathematics | The product of the prime integers between 53 and 60, inclusive, is: | [
"50! – 40!",
"178,239",
"2,303",
"2,021",
"2,000"
] | only prime number bet ween 53 and 60 inclusive are 53, 57, 59
thus 53*57 * 59= 178,239
Ans: B
The answer is: B | B |
mathematics | Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 2 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last ye... | [
"1/7",
"1/6",
"1/5",
"1/4",
"1/3"
] | Suppose the portion of her salary that she saved is X
and the remaining portion is Y
X+Y= total take home salary
given, 12X = 2Y
or 6X = Y
Total take-home salary= X+ 6X= 7X
hence, she saved 1/7-th portion of her take home salary
A
The answer is: A | A |
mathematics | A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1800. The difference between the profit shares of A and C is? | [
"720",
"266",
"155",
"600",
"441"
] | Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1800
=> 5 parts out of 15 parts is Rs. 1800
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1800) = Rs. 720
Answer:A
The answer is: A | A |
mathematics | A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics? | [
"11",
"66",
"77",
"80",
"71"
] | Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80
Answer:D
The answer is: D | D |
mathematics | Donna, Chris, and Austin have a total of $93 in their wallets. Donna has $7 more than Chris. Austin has 3 times what Donna has. How much do they have in their wallets? | [
"Donna $10 -Chris $45 -Austin $90",
"Donna $20-Chris $13 -Austin $60",
"Donna $30 -Chris $34-Austin $70",
"Donna $40 -Chris $56 -Austin $100",
"Donna $50 -Chris $23 -Austin $80"
] | Let the amount in Chris’s wallet be $x
Donna has $7 more than Chrish's wallet = $(x + 7)
Austin has 3 times than Donna's wallet = $3(x + 7)
According to the problem, Donna, chris, and Austin have a total of $93 in their wallets.
Therefore,
x + (x + 7) + 3(x + 7) = 93
x + x + 7 + 3x + 21 = 93
5x + 28 = 93
- 28 -28 (subt... | B |
mathematics | Which of the following is a prime number | [
"18",
"20",
"19",
"16",
"24"
] | Clearly, 19 is a prime number.
Option C
The answer is: C | C |
mathematics | A shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth? | [
"Rs.59",
"Rs.58",
"Rs.09",
"Rs.50",
"Rs.13"
] | SP per metre = 18000/400
= Rs. 45 Loss per metre
= Rs. 5 CP per metre = 45 + 5
= Rs.50
Answer: D
The answer is: D | D |
mathematics | In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is: | [
"1 hour",
"2 hours",
"3 hours",
"4 hours",
"5 hours"
] | Let the duration of the flight be x hours
600/x - 600 (x+1/2)= 200
600/x - 1200/(2x+1) = 200
x(2x + 1) = 3
2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x can't be negative hence x=1
x = 1 hr.
Duration =1 hr
ANSWER:A
The answer is: A | A |
mathematics | Two airplanes take off from one airfield at noon. One flies due east at 202 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.? | [
"166",
"332",
"400",
"483",
"404"
] | E
In two hours:
the plane flying East will be 404 miles away from airport.
the other plane will be 566 miles away from airport.
566/404 = ~1.4 = ~sqrt(2)
This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 404 miles apart. E
The answer is: E | E |
mathematics | What number times (1⁄4)^2 will give the value of 4^3? | [
"4",
"16",
"64",
"256",
"1024"
] | x*(1/4)^2 = 4^3
x = 4^2*4^3 = 4^5 = 1024
The answer is E.
The answer is: E | E |
mathematics | the age of a and b are in the ratio 4:5 and of b and c in the ratio 3:2.the youngedt of three is | [
"a",
"b",
"c",
"can't say",
"none"
] | a:b => 4:5 3*(a:b)=> 12:15
b:c=>3:2 5*(b:c)=> 15:10
a:b:c =>12:15:10
Therefore youngest is c.
ANSWER:C
The answer is: C | C |
mathematics | A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, the how old is B? | [
"7",
"9",
"18",
"11",
"10"
] | Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 47
⇒ 5x = 45
⇒ x = 9.
Hence, B's age = 2x = 18 years.
Answer: C
The answer is: C | C |
mathematics | Eleven years ago Tina was half as old as Ike will be in 4 years. If Ike is m years old now, how old is Tina now, in terms of m? | [
"4m - 11",
"m/2 + 13",
"1/(2m - 22)",
"(4m + 11)/2",
"2m-7"
] | Ike's current age = m
Ike's age after 4 years = m + 4
Tina age 11 years ago =(m+4)/2
Tina's current age = (m+4)/2 + 11 = (m+4+22)/2= m/2+13
Ans B
The answer is: B | B |
mathematics | 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 48 days. If 40 more cows and 15 more buffaloes are brought in, how many days will the fodder last? | [
"20",
"24",
"28",
"32",
"36"
] | 2 oxen = 3 buffaloes = 4 cows
Also: 15 buffaloes + 8 oxen + 24 cows
= 10 oxen + 8 oxen + 12 oxen = 30 oxen
There is enough fodder for 1 oxen for 30*48 days.
40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen
The new total is equal to 60 oxen instead of 30 oxen.
30*48 / 60 oxen = 24 days
The answer is B.
The answer is... | B |
mathematics | Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 50% Vermouth by volume. How many ounces of Gin must he add? | [
"n/6",
"n/3",
"3n/5",
"5n/6",
"8n/5"
] | 4 ounces is vermouth
6 ounces of gin...
Total volume 10.
To make vermouth account for 50% of total volume the new volume must be....
x*0.5=4
x=8 ounces....
So now you see that he must add 2 ounces of gin...
Plug in 6 for n in the answer choices and look for answer 2
B
The answer is: B | B |
mathematics | If the average (arithmetic mean) of a and b is 140, and the average of b and c is 100, what is the value of a − c? | [
"−220",
"−100",
"100",
"135",
"80"
] | a+b = 280
b+c = 200
a-c = 80.
IMO option E.
The answer is: E | E |
mathematics | A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: | [
"3:4",
"3:5",
"4:5",
"16:15",
"12:13"
] | For an income of $1 in 9% stock at 96, investment =$(96/9)=32/3
For an income of $1 in 12% stock at 120, investment =$(120/12)
=$10
Ratio of investment=32/3:10
=16:15
Option D
The answer is: D | D |
mathematics | A freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later a
passenger train leaves the same station for Chicago traveling 60 mph. How long before the
passenger train overtakes the freight train? | [
"6hours",
"5hours",
"9ours",
"2hours",
"4 hours"
] | Read the problem. It is a time, rate, and distance problem. (Use D=r*t)
The question asks, “how long?” (which means time) for the passenger train.
Let t=the time it takes the passenger train to overtake the freight train
t+2=the number of hours the freight train had traveled when overtaken.
Draw a sketch and make a tab... | E |
mathematics | A man can row downstream at the rate of 24 Kmph and upstream at 7 Kmph. Find the man’s rate in still water and rate of current? | [
"8.5",
"8.0",
"9.5",
"9.0",
"8.25"
] | Rate of still water = 1/2 (down stream + upstream)
= 1/2 (24 + 7) = 15.5 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (24 - 7)
= 1/2 (17)
= 8.5 kmph
Answer is A.
The answer is: A | A |
mathematics | Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of R... | [
"Rs.45,000",
"Rs.50,000",
"Rs.90,000",
"Rs.75,000",
"none"
] | Solution
Sekar:Rajeev:Jatin= (25000×12+35000×12+45000×12):(35000×24) : (35000×12)
= 1260000 : 840000 : 420000
= 3 : 2 : 1.
Rajeev's share =Rs.(270000×2/6)
= Rs.90000.
Answer C
The answer is: C | C |
mathematics | A man can row 7 ½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place? | [
"1.5 km",
"1 km",
"2.5km",
"2 km",
"3 km"
] | Speed downstream =(7.5+1.5)km/hr=9 km/hr;
Speed upstream=(7.5-1.5)kmph=6kmph.
Let the required distance be x km.then,
x/9+x/6=50/60.
2x+3x=(5/6*18)
5x=15
x=3.
Hence,the required distance is 3km.
Answer is E.
The answer is: E | E |
mathematics | Find the value of 72515 x 9999 = m? | [
"345434667",
"246465757",
"465767867",
"725077485",
"645354643"
] | 72515 x 9999 = 72515 x (10000 - 1)
= 72515 x 10000 - 72515 x 1
= 725150000 - 72515
= 725077485
D
The answer is: D | D |
mathematics | If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is: | [
"50 km",
"56 km",
"70 km",
"80 km",
"85 km"
] | Let the actual distance travelled be x km.
Then, x/10 = (x + 20)/14
=14x = 10x + 200
4x = 200
x = 50 km.
Answer :A
The answer is: A | A |
mathematics | If a(a + 2) = 120 and b(b + 2) = 120, where a ≠ b, then a + b = | [
"-4",
"-6",
"-2",
"-10",
"-8"
] | i.e. if a = 10 then b = -12
or if a = -12 then b = 10
But in each case a+b = -12+10 = -2
Answer:C
The answer is: C | C |
mathematics | Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is? | [
"4:7",
"4:3",
"4:0",
"4:2",
"4:6"
] | Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9
= 4:3
Answer:B
The answer is: B | B |
mathematics | A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 20 percent of the pack would be outfielder cards? | [
"10",
"5",
"6",
"7",
"8"
] | let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 20% of toatal Ocards
12-X<.2*12
X>12-2.4
X>9.6
X=10
Ans A
The answer is: A | A |
mathematics | 78 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? | [
"10",
"13",
"26",
"15",
"16"
] | Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 78 :: 12 : x
Working hours/day 6 : 5
30 x 6 x x = 78 x 5 x 12
x = (78 x 5 x 12)/(30 x 6)
x = 26.
ANSWER:C
The answer is: C | C |
mathematics | If x% of y is 100 and y% of z is 200, then find the relation between x and z. | [
"z = x",
"2z = x",
"z = 2x",
"z =x2",
"None of above"
] | Explanation:
It is , y% of z = 2(x% of y)
=> yz/100 = 2xy/100
=> z = 2x
Answer: Option C
The answer is: C | C |
mathematics | Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 15 years? | [
"30",
"35",
"40",
"50",
"60"
] | Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 15 years = (20 + 15) years =35 years.
Answer : B
The answer is: B | B |
mathematics | The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B>A and B-A is perfectly divisible by 7, then which of the following is necessarily true? | [
"100<A<299",
"106<A<305",
"112<A<311",
"118<A<317",
"None"
] | Explanation:
Let A = abc the B = cba
Given, B – A is exactly divisible by 7.
Therefore, 100c + 10b + a – (100a + 10b + c) = 99c – 99a = 99(c – a)
So 99(c – a) should be divisible by 7.
We know that 99 is not divisible by 7. So (c – a) should be divisible by 7 which implies c – a is 0, 7, 14...
c – a = 0 is not possible... | B |
mathematics | Find the odd man out
4, 9,16, 36, 64, 144 | [
"144",
"16",
"9",
"36",
"4"
] | 9 is square of 3 which is odd number where as all others are squares of even numbers.
ANSWER:C
The answer is: C | C |
mathematics | After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 74%?
M13-03. | [
"N−35",
"N+72",
"2N+76",
"2N+70",
"2N−35"
] | Say N=1.
So, after 1 test John has 70 correct answers.
In 2 tests, so in 200 questions he needs to have 0.74*200=148 correct answers, so in the second test he must get 148-70=78 questions correctly.
Now, plug N=1 into the answer choices to see which one yields 78. Only option D fits.
Answer: C.
The answer is: C | C |
mathematics | A student completes a 3 part exam as follows. The student completes sections A in 4 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour? | [
"10:3",
"9:2",
"7:1",
"8:3",
"11:2"
] | The time spent on section B and section C is 28 minutes each.
The ratio of C to A is 28:4 = 7:1
The answer is C.
The answer is: C | C |
mathematics | The distance between two cities A and B is 465 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet? | [
"09",
"07",
"12",
"05",
"03"
] | Explanation:
Suppose they meet x hrs after 8 a.m
then,
[Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 465
Therefore, 60x + 75(x-1) = 465
=> x=3.
So,they meet at (8+4) i.e, 12 noon
Answer: C)
The answer is: C | C |
mathematics | If f(x) = k(x - k) and k is a constant, what is the value of f(6) - f(2), in terms of k? | [
"1",
"4k",
"7k - 1",
"k^2 + k",
"k^2 - k"
] | First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(6) and f(2):
f(6) = k(6) - k^2 = 6k - k^2
f(2) = 2k - k^2
Answer B
The answer is: B | B |
mathematics | What is the probability of getting at least one six in a single throw of three unbiased dice? | [
"1/6",
"125/216",
"1/36",
"81/216",
"91/216"
] | Find the number of cases in which none of the digits show a '6'.
i.e. all three dice show a number other than '6', 5 * 5 *5 = 125 cases.
Total possible outcomes when three dice are thrown = 216.
The number of outcomes in which at least one die shows a '6' = Total possible outcomes when three dice are thrown - Number of... | E |
mathematics | What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 145° each? | [
"96 cm",
"108 cm",
"120 cm",
"132 cm",
"154.28 cm"
] | Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 145*n
from here
n = 10.28
So perimeter becomes 15*10.28= 154.28
Answer: E
The answer is: E | E |
mathematics | Souju's age is 150% of what it was 10 years ago, but 75% of what it will be after 10 years. What is her present age? | [
"25 years",
"27years",
"30 years",
"42 years",
"66 years"
] | Let the age before 10 years =x. Then,
150x/100=x+10
⇒150x=100x+1000
⇒x=1000/50=20
Present age =x+10=20+10=30
ANSWER:C
The answer is: C | C |
mathematics | Income of A is 25% more than the income of B. What is the income of B in terms of income of A? | [
"80%",
"75%",
"78.66%",
"71.25%",
"None of these"
] | Explanation:
One of the most basic questions.
Let income of B be 100. Income of A is 25% more than income of B which means Income of A becomes 125
Now income of B in terms of A = 100/125 *100 = 80%
ANSWER A
The answer is: A | A |
mathematics | A miniature gumball machine contains 4 blue, 3 green, and 3 red gumballs, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color? | [
"2/5",
"3/5",
"3/10",
"7/30",
"11/30"
] | The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 4*3*3=36.
P(dispensing one of each color)=36/120=3/10.
The answer is C.
The answer is: C | C |
mathematics | The diameter of a wheel of cycle is 21 cm. It moves slowly along a road. How far will it go in 500 revolutions? | [
"260 m",
"290 m",
"320 m",
"330 m",
"380 m"
] | In revolution, distance that wheel covers = circumference of wheel Diameter of wheel = 21 cm
Therefore, circumference of wheel = πd
= 22/7 × 21
= 66 cm
So, in 1 revolution distance covered = 66 cm
In 500 revolution distance covered = 66 × 500 cm
= 33000 cm
= 33000/100 m
= 330 m
Answer : option D
The answer is: D | D |
mathematics | A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? | [
"A",
"B",
"C",
"D",
"ALL"
] | Answer: Option C
Let b = 100
a = 50
c * (150/100) = 50
3c = 100
c = 33.3 then 'c' cheapest
The answer is: C | C |
mathematics | Find the last non-zero digit of 30^2345 | [
"1",
"2",
"3",
"4",
"5"
] | 30^2345=(3*10)^2345=3^2345*10^2345
so 30^2345 has 2345 zeroes,the last non-zero digit of 30^2345 will be same as unit digit of 3^2345
3^2345=3^(4*586+1)=> 3^1=3
last non-zero digit of 30^2345= 3
ANSWER:C
The answer is: C | C |
mathematics | Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word BANANA could be arranged to create a six-letter code? | [
"6!",
"6! − (3! + 2!)",
"6! − (3! × 2!)",
"6!/(3! + 2!)",
"6!/(3! × 2!)"
] | Number of letters in word 'BANANA' = 6.
The letters 'A' and 'N' appear 3 times and 2 times respectively in the word 'BANANA'.
Therefore the mathematical solution for number of ways that the letters of the word BANANA can be arranged to create six-letter code
= 6!/(3!*2!)
Answer: E
The answer is: E | E |
mathematics | How many cubes of 3cm edge can be cut out of a cube of 18cm edge | [
"36",
"232",
"216",
"484",
"None of these"
] | Explanation:
number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216
Answer: C
The answer is: C | C |
mathematics | For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 980, what i... | [
"16",
"14",
"18",
"10",
"20"
] | we know that : x > 1, y > 1, and x + 3y < 980,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest no all factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10... | A |
mathematics | A man is 18 years older than his son. In eight years, his age will be twice the age of his son. The present age of this son is | [
"5 years",
"10 years",
"15 years",
"20 years",
"25 years"
] | Explanation:
Let's Son age is x, then Father age is x+18.
=> 2(x+8) = (x+18+8)
=> 2x+16 = x+26
=> x = 10 years
Answer: Option B
The answer is: B | B |
mathematics | log3 N+log15 N what is 3 digit number N that will be whole number | [
"3375",
"7292",
"8291",
"3929",
"2727"
] | No of values N can take is 1
15^3=3375
ANSWER:A
The answer is: A | A |
mathematics | A regular octagon is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ? | [
"48 degrees",
"54 degrees",
"67.5 degrees",
"84 degrees",
"108 degrees"
] | its a regular pentagon so divide the globe by 8.
= 360/8
= 45
45 would be the angle at O.
Angles at A and B are equivalent, so
45 + 2x = 180
2x = 135
x = 67.5
Angles OAB and OBA will be 67.5 degrees each.
C
The answer is: C | C |
mathematics | The difference of the squares of two consecutive even integers is divisible by which of the following integers ? | [
"3",
"4",
"6",
"7",
"9"
] | Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
ANSWER B
The answer is: B | B |
mathematics | By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ? | [
"16",
"18",
"20",
"22",
"25"
] | Explanation:
Let S.P. of 45 lemons be Rs. x.
Then, 80 : 40 = 120 : x or x =40X120/80=60
For Rs.60, lemons sold = 45
For Rs.24, lemons sold =45/60X24=18.
ANSWER IS B
The answer is: B | B |
mathematics | Carol spends 1/4 of her savings on a stereo and 1/3 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? | [
"1/4",
"2/7",
"5/12",
"1/2",
"7/12"
] | Total Savings = S
Amount spent on stereo = (1/4)S
Amount spent on television = (1-1/3)(1/4)S = (2/3)*(1/4)*S = (1/6)S
(Stereo + TV)/Total Savings = S(1/4 + 1/6)/S = 5/12
Answer: C
The answer is: C | C |
mathematics | Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 60900. What is his profit percent? | [
"10.7%",
"19%",
"18%",
"14%",
"16%"
] | Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP
= Rs. 60900
Profit(%) = (60900 - 55000)/55000 * 100
= 10.7%
Answer: A
The answer is: A | A |
mathematics | Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 5 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? | [
"1 ≤ n ≤23",
"3 ≤ n ≤21",
"6 ≤ n ≤18",
"5 ≤ n ≤19",
"9 ≤ n ≤15"
] | ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+5-2+3=18 for the maximum, and 12-5+2-3=6 for the minimum, so C is the answer
The answer is: C | C |
mathematics | A and B invested in a business. They earned some profit which they divided in the ratio of 2:3. If A invested Rs.40, 000, the amount invested by B is: | [
"Rs. 65,000",
"Rs. 70,000",
"Rs. 80,000",
"Rs. 90,000",
"Rs. 60,000"
] | Invested by B = 40000/2*3 = 60000
Answer : E
The answer is: E | E |
mathematics | By selling 12 toffees for a rupee, a man loses 20%. How many for a rupee should be sell to get a gain of 20%? | [
"5",
"8",
"10",
"15",
"20"
] | Explanation:
Let S.P. of 12 toffees be Rs. x.
Then, 80:1 = 120:x or x = 120/180 = 3/2
For Rs. 3/2, toffees sold = 12.
For Re. 1, toffees sold = 12 * 2/3 = 8
ANSWER IS B
The answer is: B | B |
mathematics | A basketball player practices 2 hours a day Monday through Friday. How many hours must he practice Saturday and Sunday combined if he wants to practice an average (arithmetic mean) of 3 hours a day for the seven day week? | [
"8",
"9",
"10",
"11",
"12"
] | Total number of hours practiced Mon through Fri: 5*2 = 10
Total number of hours that will be practiced in a 7 day week considering 3 hours a day average: 7*3 = 21
thus 21-10 = 11 hours still need to be practiced (on Sat and Sun combined)
D
The answer is: D | D |
mathematics | Find the simple interest on Rs. 3000 at 6 1/4% per year for the period from 4th Feb., 2005 to 18th April, 2005. | [
"36.5",
"33.5",
"35.5",
"37.5",
"None of them"
] | Time = (24+31+18)days = 73 days = 73/365 years = 1/5 years.
P = Rs.3000 and R = 6 ¼ %p.a = 25/4%p.a
Therefore, Simple Interest. = Rs.(3,000*(25/4)*(1/5)*(1/100))= Rs.37.50.
Answer is D.
The answer is: D | D |
mathematics | A quadratic function f(x) attains its minimum value of -15 at x=3. If f(0)=5, find the value of f(9). | [
"65",
"55",
"-25",
"75",
"25"
] | Explanation :
Any quadratic equation can be written as f(x) = α(x-k)2 - β
Given that minimum value of f(x) is -15 at x=3
f(x) is minimum when x=k => k=3
-15=-β => β= 15
Also given that f(0) = 5
=> 5 = α(0-3)2 - 15 => α= 20/9
Hence, f(9)=20/9(9-3)2 - 15 = 65
Answer : A
The answer is: A | A |
mathematics | Without any stoppages a person travels a certain distance at an average speed of 40 km/hr and with stoppages he covers the same distance at an average of 20 km/hr. How many minutes per hour does he stop? | [
"15 minute",
"20 minutes",
"30 minutes",
"45 minutes",
"None of these"
] | Explanation :
In one hour the distance covered at actual speed = 40km and with stoppages it covers only 20 km
so to travel 20 km at original speed i.e. 20 = 40*t, so t = 1/2 hour = 30
minutes
Answer – C
The answer is: C | C |
mathematics | If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number? | [
"10",
"20",
"25",
"30",
"35"
] | 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
B)
The answer is: B | B |
mathematics | Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present ages? | [
"35",
"38",
"37",
"36",
"30"
] | Let present age of P and Q be 3x and 4x respectively.
Ten years ago, P was half of Q's age
⇒(3x−10)=12(4x−10)⇒6x−20=4x−10⇒2x=10⇒x=5
Total of their present ages
=3x+4x=7x=7×5=35
Answer is A.
The answer is: A | A |
mathematics | In what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way? | [
"8 sec",
"7 sec",
"2 sec",
"6.5 sec",
"9 sec"
] | T = 65/36 * 18/5
= 6.5 sec
Answer:D
The answer is: D | D |
mathematics | There are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed. | [
"40",
"49",
"41",
"56",
"42"
] | First of all you should remember that there is a difference in left and right sock.
now no. of way to select any of the sock = 7
and for second = 6
so total methods = 7*6 = 42
ANSWER:E
The answer is: E | E |
mathematics | In what time will a train 100 m long cross an electric pole, it its speed be 126 km/hr? | [
"2.5",
"2.9",
"2.4",
"2.85",
"2.1"
] | Speed = 126 * 5/18 = 35 m/sec
Time taken = 100/35
= 2.85 sec.
Answer:D
The answer is: D | D |
mathematics | When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 39? | [
"3",
"8",
"12",
"32",
"35"
] | n = 5p + 1 = 6,11,16,21,26,31
n = 7q + 3 = 3,10,17,24,31
=>n = 39m + 31
To get this, we need to take LCM of co-efficients of p and q and first common number in series.
So we need to add 8 more to make it
39m + 39
Answer - B
The answer is: B | B |
mathematics | Arun borrowed a sum for 4 years on S.I. at 12%. The total interest paid was Rs. 360. Find the Principal. | [
"120",
"360",
"480",
"560",
"750"
] | P=100×SI/RT=100×360/12×4
=100×30/4
=25×30
=750
Option E
The answer is: E | E |
mathematics | A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minutes ahead of scheduled. If it made 50 km/hr, then by the scheduled time of arrival it would still have 40 km more to go to station B. Find:
A) The distance between the two stations;
B) The time ... | [
"34",
"27",
"26",
"28",
"60"
] | Let xx be the scheduled time for the trip from A to B. Then the distance between A and B can be found in two ways. On one hand, this distance equals 75(x−4860)75(x−4860) km. On the other hand, it is 50x+4050x+40 km. So we get the equation:
75(x−4860)=50x+4075(x−4860)=50x+40
x=4x=4 hr is the scheduled travel time. The d... | E |
mathematics | A , B , and C started a partnership business by investing $27,000 , $72,000 , and $81,000 respectively. At the end of the year , the profit was distributed among them. If C's share of profit is $18,000, what is the total profit? | [
"$24,000",
"$32,000",
"$40,000",
"$48,000",
"$56,000"
] | A:B:C = 27000:72000:81000 which is a ratio of 3:8:9.
Let the total profit be x.
x * 9/20 = 18000
x = 18000*20/9 = 40,000.
The answer is C.
The answer is: C | C |
mathematics | If the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new numbers is : | [
"22",
"40",
"88",
"27",
"11"
] | Explanation:
Let the numbers are
By Hypothesis , ......(i)
Mean of new numbers =
By (i)
Answer: B) 40
The answer is: B | B |
mathematics | What is the median from the below series
77, 72, 68, 76, 78, 88, 84, 86, and 81 | [
"72",
"76",
"78",
"77",
"81"
] | Ordering the data from least to greatest, we get:
68, 72, 76, 77, 78, 81, 84, 86, 88
The median numbers was 78. (Four number were higher than 78 and four were lower.)
C
The answer is: C | C |
mathematics | Which of the following is between 27/37 and 29/35? | [
"1/3",
"3/8",
"1/2",
"5/8",
"7/9"
] | I see this as a POE (Process of Elimination) and Ballparking (Estimation) question. Not sure if this is the most efficient, but it worked:
1) I estimate 27/37 to be ~3/4+ (approximately slightly greater than 3/4)
2) I estimate 29/35 to be ~4/5+ (approximately slightly greater than 4/5)
3) So now I'm looking for an answ... | E |
mathematics | Mangala completes a piece of work in 12 days, Raju completes the same work in 36 days. If both of them work together, then the number of days required to complete the work is | [
"6 days",
"7 days",
"8 days",
"9 days",
"11 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 = 12 × 36/48 = 9 days.
D
The answer is: D | D |
mathematics | A semicircular shaped window has diameter of 63cm. Its perimeter equals | [
"162",
"766",
"298",
"277",
"198"
] | Explanation:
perimeter of window = {\color{Blue} \Pi }r+2r
= [{(22/7) * (63/2)} +63]
= 99+63
= 162 cm
Answer: A) 162
The answer is: A | A |
mathematics | If pq > 0, which of the following must be negative? | [
"p/q",
"-p/q",
"-p/-q",
"-p * -q",
"pq"
] | Given pq> 0 So both will be the positive integers. If both are positive, then A,C,D,E also positive.
Answer :B
The answer is: B | B |
mathematics | If q = 50! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 29
III. 41 | [
"I only",
"III only",
"II and III",
"I and II",
"I, II, and III"
] | The numbers 11, 29, and 41 are all factors of 50!
Therefore they can not be factors of 50! + 1.
The answer is E.
The answer is: E | E |
mathematics | The difference between a two digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number? | [
"2",
"3",
"4",
"8",
"9"
] | Solution
Let the ten's digit be x and units digit be y.
Then, (10x+y) - (10y+x)= 36 ‹=›9(x - y) = 36
‹=›x - y = 4.
Answer C
The answer is: C | C |
mathematics | What is the value of 4^5+4^8? | [
"4^12",
"4^35",
"17(4^5)",
"8^12",
"65(4^5)"
] | 4^5+4^8
=4^5(1+4^3)
=4^5 * 65
Answer E
The answer is: E | E |
mathematics | Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? | [
"7.18",
"7.12",
"7.1",
"7.15",
"7.11"
] | T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer:D
The answer is: D | D |
mathematics | The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was : | [
"12003",
"12000",
"12002",
"12289",
"12019"
] | Explanation:
= Rs.12000
Answer: B) 12000
The answer is: B | B |
mathematics | A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 5 more days. How many days would it have taken the second carpenter to do the complete job working alone? | [
"4.5",
"7.5",
"9.5",
"17.5",
"24.5"
] | A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/7 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 5 days @ rate=1/x per day
Exp... | D |
mathematics | At a certain college there are twice as many history majors as English majors and three times as many history majors as mathematics majors. What is the ratio of the number of english majors to the number of mathematics majors? | [
"6 to 1",
"2 to 3",
"3 to 2",
"1 to 5",
"1 to 6"
] | This is how I translated the question:
At a certain college there are twice as many english majors as history majors
H = 2E
and three times as many english majors as mathematics majors.
H = 3M
What is the ratio of the number of history majors to the number of mathematics majors?
What is E:M?
Just set E equal to each ot... | C |
mathematics | Thomas bought a pack of eleven computers for Rs. 500000 and sold it for Rs.550000. What is the % of profit he is making per computer? | [
"10",
"14",
"19",
"21",
"25"
] | The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5
The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0
Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5
The % of profit in selling a single computer=(4545.5/45454.5)*100=10%
Answer:A
The answer is: A | A |
mathematics | Find the number of divisors of 1728.? | [
"26",
"27",
"28",
"29",
"30"
] | 1728= 2^6 * 3^3
Hence the Number of factors = (6+1) x (3+1) = 7 x 4 = 28.
We know that if a number represented in standard form (a^m *b^n) , then the number of factors Is given by (m+1)(n+1).
Answer is 28
ANSWER:C
The answer is: C | C |
mathematics | If $100 invested at a certain rate of simple interest amounts to $140 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years? | [
"$190",
"$180",
"$200",
"$240",
"$270"
] | 100 amounts to 140 in 3 years.
i.e (principal + interest ) on 120 in 3 years = 140
100 + 100*(r/100)*(3) = 140 => r = 40/3
150 in 6 years = principal + interest
= 150 + 150*(r/100)*(6)
= 270
Answer is E.
The answer is: E | E |
mathematics | Bob invested $2000 in fund A and $1000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after bob made these investments. Bob's investment in fund A was worth ... | [
"$500",
"$550",
"$600",
"$650",
"$700"
] | Bob earned 2000*(1+0.12) in total by fund A and earned 1000*(1+0.3)^2 in total by fund B.
So 2000*(1.12) - 1000*(1.69)= 550.
The answer is, therefore, (B).
The answer is: B | B |
mathematics | What least number must be added to the least number of six digits so that the resulting number may be a perfect square. | [
"489",
"267",
"278",
"199",
"111"
] | The least number of six digits = 100000 3 10 00 00 317 9 61 100 61 627 3900 4389 – 489 Least number to be added = 489.
Answer:A
The answer is: A | A |
mathematics | The area of a square is equal to five times the area of a rectangle of dimensions 50 cm * 10 cm. What is the perimeter of the square? | [
"289 cm",
"200 cm",
"829 cm",
"288 cm",
"289 cm"
] | Area of the square = s * s
= 5(50 * 10)
=> s = 50
= 50 cm
Perimeter of the square
= 4 * 50
= 200 cm.
Answer: B
The answer is: B | B |
mathematics | The total age of A and B is 15 years more than the total age of B and C. C is how many years younger than A ? | [
"12",
"27",
"15",
"18",
"11"
] | (A+B) - (B+C) = 15
A - C = 15.
C is younger than A by 15 years.
Answer: C
The answer is: C | C |
mathematics | The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. | [
"40",
"28",
"29",
"26",
"20"
] | Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 60 and C - P = 20 M + C / 2
= [(M + P) + (C - P)] / 2
= (60 + 20) / 2 = 40.
Answer:A
The answer is: A | A |
mathematics | If 1 + 9 + 11 = 1, Then what is the value of
12 + 11 + 9 = ? | [
"9",
"11",
"12",
"13",
"10"
] | E
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1
Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)
The answer is: E | E |
mathematics | If f is a function defined for all k by f(k) = k^5 /16, what is f(3k) in terms of f(k)? | [
"1/8 f(k)",
"5/8 f(k)",
"244 f(k)",
"243 f(k)",
"323 f(k)"
] | f(k) = k^5 /16
f(3k) = (3k)^5/16 = 243 * k^5 /16 = 243 * (k^5 /16) = 243 f(k).
So answer is D.
The answer is: D | D |
mathematics | 3x^2-6x+3 = 0 Find the above equation find the value of x | [
"0",
"1",
"2",
"3",
"4"
] | a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
The answer is: B | B |
mathematics | If x^2 - y^2 = 2xy, then (x+y)^2 = | [
"2x^2",
"3x^2",
"4xy",
"2y^2",
"-y^2"
] | Its B
x^2 -y^2 = 2xy
x^2 = 2xy + y^2
Add x^2 on both sides we get
x^2 +x^2 = x^2 +y^2 +2xy
2x^2 = (x+y)^2
Correct Option : A
The answer is: A | A |
mathematics | A jar contains 8 marbles consisting of an equal number of red, green, and blue marbles. Four marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the four marbles have been removed? | [
"1/495",
"1/165",
"3/70",
"1/35",
"11/20"
] | Jar contains {4-red, 4-green, 4-blue} marbles. We are asked to find the probability that after removing 4 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.
Sample space = 8C4 = 495.
Probability of choosing 4 red = 4C4/8C4 = 1/70.
Probability of choosing 4 green =... | C |
mathematics | How many boxes do we need if we have to carry 250 apples into boxes that each hold 25 apples? | [
"A)9",
"B)5",
"C)7",
"D)10",
"E)None of the above"
] | Sol.
Apples 250
Each carries 25
= 250/25
= 10
Answer : D
The answer is: D | D |
mathematics | 7, 35, 56, 91, 126
In the sequence above, each term is related with the others. Which of the following could not be a term in the sequence? | [
"398",
"259",
"322",
"686",
"847"
] | Simplifying the question into easier words we just need to find which of the numbers is not divisible by 7
clearly the answer is 398 because if we divide 398 by 7 we get a remainder of 56.85
Correct answer - A
The answer is: A | A |
mathematics | The speed of the boat in still water in 12 kmph. It can travel downstream through 54 kms in 3 hrs. In what time would it cover the same distance upstream? | [
"8 hours",
"6 hours",
"4 hours",
"5 hours",
"9 hours"
] | Still Water=12km/hr
Downstream=54/3=18km/hr
Upstream=>> still water=(u+v/2) =>> 12=u+18/2 = 6km/hr
So time taken in upstream = 545/6 =9hrs
ANSWER:E
The answer is: E | E |
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