subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | In the word CONTRACTUAL, the positions of the first and the eleventh letters are interchanged. Similarly, the positions of the second and the tenth letters are interchanged, and so on, up to the positions of fifth and seventh letters are interchanged, keeping the position of sixth letter unchanged. Which letter will be... | [
"U",
"N",
"T",
"A",
"None of these"
] | New word will be LAUTCARTNOC
6th letter from the left end is A,and and 3rd to the righ of thet letter is N.
ANSWER:B
The answer is: B | B |
mathematics | Two trains 135 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? | [
"7.45",
"7.16",
"7.12",
"7.15",
"7.11"
] | T = (135 + 165)/ (80 + 65) * 18/5
T = 7.45
Answer: A
The answer is: A | A |
mathematics | WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 7/8 probability that task 1 will be completed on time, and a 1/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task ... | [
"1/20",
"3/40",
"13/40",
"7/10",
"13/22"
] | P(1 and not 2)=7/8*(1-1/5)=7/10.
Answer: D.
The answer is: D | D |
mathematics | The average of ten numbers is 8. If each number is multiplied by 12, then what is the average of the new set of numbers? | [
"8",
"12",
"20",
"96",
"120"
] | The sum of the ten numbers is 8*10 = 80
If each number is multiplied by 12, the new sum is 12*(80).
The average is then 12*8 = 96
The answer is D.
The answer is: D | D |
mathematics | The original price of a car was $30,000. Because the car owner thought he could get more money for the car, he set a new price by increasing the original price of the car by 10%. After a week, the car had not sold, so the owner discounted the new price by 10%, and the car was finally sold. What price was the car sold f... | [
"$29,660",
"$29,680",
"$29,700",
"$29,720",
"$29,740"
] | The car was sold for (0.9)(1.1)($30,000)=$29,700.
The answer is C.
The answer is: C | C |
mathematics | An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 56$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold? | [
"52",
"75",
"60",
"136",
"184"
] | w1/w2 = (A2 - Aavg)/(Aavg - A1) = (56 - 40)/(40 - 36) = 16/4 = 4/1 = Number of MicroTron stocks/Number of Dynaco stocks
So for every 4 MicroTron stock, she sold 1 Dynaco stock.
So out of 300 total stocks, (1/5)th i.e. 300/5 = 60 must be Dynaco stock.
Answer (C)
The answer is: C | C |
mathematics | The least number by which 72 must be multiplied in order to produce a multiple of 112, is | [
"6",
"12",
"14",
"18",
"20"
] | Solution
Required numbers is divisible by 72 as well as by 112, if it is divisible by their LCM, which is 1008.
Now, 1008 when divided by 72, gives quotient = 14.
Required number = 14.
Answer C
The answer is: C | C |
mathematics | The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? | [
"16 seconds",
"34 seconds",
"14 seconds",
"12 seconds",
"15 seconds"
] | Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5
= 12 seconds.
Answer: D
The answer is: D | D |
mathematics | What is the remainder if 7^12 is divided by 100? | [
"1",
"2",
"3",
"4",
"5"
] | 7^16 can be written as (7^4)^3
If we divide 7^4 by 100 the reminder is 1
So, (7^4)^3 by 100, the reminder is 1^3 = 1
Answer : A
The answer is: A | A |
mathematics | How much interest can a person get on Rs. 4500 at 20.1% p.a. simple interest for a period of seven years and six months? | [
"6783.74",
"6783.75",
"6783.76",
"6783.77",
"6783.78"
] | I = (4500 * 7.5 * 20.1)/100
= (4500 * 15 * 20.1)/(100 * 2 )
= Rs. 6783.75
Answer: B
The answer is: B | B |
mathematics | Tom started a new grocery store business. During his first month he bought groceries for $650$650 and sold them for $800$800, while in the second month he bought with $800$800 and sold for $1200$1200. We need to know if Tom made more profit or not and profit or loss percentage | [
"50 % loss",
"50% Profit",
"40 % loss",
"60 % Profit",
"None"
] | Solution:
We cannot directly tell from these numbers if Tom's profit is increasing or not since his spending and gain are different amounts each month. In order to solve this problem we need to refer all the values to a fixed base value which is 100. Let us express the percent of his profit with respect to his expendit... | B |
mathematics | A and B together can complete a piece of work in 10days. If A alone can complete the same work in 15days, in how many days, in how many days can B alone complete that work? | [
"10",
"30",
"25",
"15",
"45"
] | (A+B)'s 1day's work = 1/10
A's 1day's work = 1/15
B's 1days's work = (1/10)-(1/15) = 1/30
Hence, B alone can complete the work in 30days.
Answer is B
The answer is: B | B |
mathematics | A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 35 revolutions, what will be the number of revolutions made by the larger wheel? | [
"15",
"12",
"21",
"9",
"22"
] | Explanation:
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
(cogs) 6 : 14 :: x : 35
⇒6×35=14 × x
⇒x = 15
Answer: Option A
The answer is: A | A |
mathematics | Statement: "You are appointed as a programmer with a probation period of 1 year and your performance will be reviewed at the end of the period for confirmation."
Assumptions:
The performance of an individual generally is not known at the time of appointment offer.
Generally an individual tries to prove his worth in the... | [
"Only assumption I is implicit",
"Only assumption II is implicit",
"Either I or II is implicit",
"Neither I nor II is implicit",
"Both I and II are implicit"
] | The performance of the individual has to be tested over a span of time as the statement mentions. So, I is implicit. The statement mentions that the individual's worth shall be reviewed (during probation period) before confirmation. So, II is also implicit.
E
The answer is: E | E |
mathematics | What percent is 50 gm of 1 kg? | [
"1.5 %",
"0.5 %",
"2.5 %",
"3.5 %",
"5 %"
] | 1 kg = 1000 gm
50/1000 × 100 = 5000/1000
=5/1 = 5 %
E)
The answer is: E | E |
mathematics | A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 40% profit on the cost o... | [
"18",
"30",
"22",
"22.5",
"27"
] | Producer price = $15;
The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 40% of the final price --> (final price)*0.6 = $18 --> (final price) = $30.
Answer: B.
The answer is: B | B |
mathematics | Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 120 pastries ? | [
"2 hours.",
"1 hours.",
"5 hours.",
"4 hours.",
"3 hours."
] | A
2 hours.
In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 120 pastries would take 120 ÷ 60 = 2 hours.
The answer is: A | A |
mathematics | If 8 people can eat a gallon of ice cream in 10 days, how long would it take 5 people to eat a gallon of ice cream? | [
"12 days",
"14 days",
"16 days",
"18 days",
"20 days"
] | 8 * 10 = 5 * x
x = 16
Answer: C
The answer is: C | C |
mathematics | Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 30 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 50 miles per hour. If both buses travel indefinitely, what is t... | [
"36",
"84",
"132",
"144",
"180"
] | 1st part: - In 1hr, Bus A covers 30 miles.
Relative speed of bus ABus B is (80-30) = 50mph.
So time required for Bus B to cover the exact distance as A is
50*t = 30
t=3/5 = 36min
2nd part
80*t=2d - B has to cover twice the distance
30*(t+1) = d - A traveled 1hr more and has to travel only only d
so
d/30 - 2d/80 = 1
D=1... | B |
mathematics | The value of land increases by r% during June and decreases by s% during July. If the value of the land is the same at the end of July as at the beginning of June, what is s in terms of r? | [
"200r/(100+2r)",
"100r/(100+r)",
"r(2+r)/(1+r)2",
"r(200+r)/10000",
"2r/r+2r"
] | The simplest pairing is a 25% increase will be offset by a 20% decrease.
Here's the proof:
Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100
So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can a... | B |
mathematics | There is a 20% chance Sandy will visit China this year, while there is a 60% chance that she will visit Malaysia this year. What is the probability that Sandy will visit either China or Malaysia this year, but NOT both? | [
"40%",
"48%",
"56%",
"64%",
"72%"
] | P(China and not Malaysia) = 0.2*0.4 = 0.08
P(Malaysia and not China) = 0.6*0.8 = 0.48
Total probability = 0.08 + 0.48 = 0.56 = 56%
The answer is C.
The answer is: C | C |
mathematics | a is an integer greater than 29 but less than 41, b is an integer greater than 39 but less than 51, what is the range of a/b? | [
"1/4",
"1/2",
"2/5",
"1",
"5/4"
] | min value of a/b will be when b is highest and a is lowest ---> a=30 and b=50
So, a/b = 3/5
max value of a/b will be when b is lowest and a is highest ---> a=40 and b=40
So, a/b = 1
Range is 1-(3/5) =2/5
Answer should be C.
The answer is: C | C |
mathematics | #p is defined as 2p+20 for any number p. What is p, if #(#(#p))=12? | [
"–16",
"–44",
"10",
"16",
"18"
] | #p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = 12 ---> 8p= -128 ---> p = -16, A is the correct answer.
The answer is: A | A |
mathematics | In how many ways can you sit 8 people on a bench if 5 of them must sit together? | [
"720",
"2,160",
"2,880",
"4,320",
"40,320"
] | In such questions, always tie the person that have to sit together. So we have effectively 3+1= 4 persons to arrange.
They can be arranged in 4! ways.
Now the 5 persons can themselves be arranged in 5! ways.
Total ways: 4!*5! = 2880.
C is the answer.
The answer is: C | C |
mathematics | In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 40 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ? | [
"64%",
"68%",
"72%",
"76%",
"80%"
] | Let in May Lee family's total income =100
in May Mrs Lee's income =60
in May rest of the family's income = 40
In june Mrs Lees income = 60*140/100 = 84
In june Total income = 84+ 40 = 124
% of Mrs Lee's income = 84/124 =67.74
(B)
The answer is: B | B |
mathematics | An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 2 ? | [
"1/9",
"1/3",
"1/2",
"2/3",
"5/6"
] | n(n+2) to be divisible by 2 either n or n+2 must be a multiples of 2.
In each following group of numbers: {1, 2, 3, 4}, {5, 6, 7, 8}, ..., {97, 98, 99, 100} there are EXACTLY 2 numbers out of 4 satisfying the above condition. For example in {1, 2, 3, 4} n can be: 2, or 4. Thus, the overall probability is 2/4 =1/2.
Answ... | C |
mathematics | If there is exactly one root of the equation 2x^2 + ax + b, where a and b are positive constants, what is b in terms of a? | [
"a/2",
"a",
"3a/2",
"a^2/8",
"a^2/4"
] | one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1
Here b = a
c= b
a = 2
substituting these values in 1, we have
a^2 = 8b => b =a^2/8
Answer is D.
The answer is: D | D |
mathematics | Raj tossed 3 dices and there results are noted down then what is the probability that Raj gets 10? | [
"27/219",
"27/216",
"27/212",
"27/211",
"27/210"
] | Always remember when 3 dice are rolled the number of ways of getting n ( where n is the sum of faces on dice)
= (n−1)C2(n−1)C2 where n = 3 to 8
= 25 where n = 9, 12
= 27 where n = 10, 11
= (20−n)C2(20−n)C2 where n = 13 to 18
The required probability = 27/3 = 27/216
Answer:B
The answer is: B | B |
mathematics | Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 5? | [
"7",
"8",
"9",
"10",
"11"
] | p is a positive even integer with a positive units digit--> the units digit of p can be 2, 4, 6, or 8 -->
In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.
Intersection of values is 6, thus the units digit of p + 5 is 6 + 5 = 1... | E |
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 28 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? | [
"457 km",
"444 km",
"547 km",
"588 km",
"653 km"
] | 1h ----- 5
? ------ 60
12 h
RS = 28 + 21 = 49
T = 12
D = 49 * 12 = 588
Answer:D
The answer is: D | D |
mathematics | A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? | [
"90",
"52",
"63",
"87",
"10"
] | Explanation:
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer:A
The answer is: A | A |
mathematics | There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected? | [
"40",
"45",
"50",
"55",
"60"
] | It's almost always better to solve "at least one" combinations/probability questions with {at least one}={total}-{none}.
Total # of selections of 4 books out of 8: C48=70C84=70;
Total # of selections of 4 hardback books out of 8 (so none paperback): C46=15C64=15;
{at least one}={total}-{none}=70-15=55.
Answer: D
The an... | D |
mathematics | The speed of a boat in still water is 12 kmph. What is the speed of the stream if the boat can cover 32 km downstream or 16 km upstream in the same time? | [
"5 kmph",
"6 kmph",
"7 kmph",
"4 kmph",
"10 kmph"
] | X = the speed of the stream
(12 + X) / (12 - X) = 2/1
12+ X = 24 - 2X
3X = 12
X = 4 km/hour
If the speed of the stream is 4km/hour, then the 'downstream' speed of the boat is 12+4 = 16km/hour and the 'upstream' speed of the boat is 12-4 = 8km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x8 = 16... | D |
mathematics | A small company reduced its faculty by approximately 13 percent to 181 employees. What was the original number of employees? | [
"A)182",
"B)208",
"C)220",
"D)224",
"E)302"
] | If x is the original number of employees, then after 13% reduction in employees number is .87x
but we are given .87x = 181
x = 208
So the original number of employees is 208
Correct Answer - B
The answer is: B | B |
mathematics | The average of six numbers is 27. If one number is excluded, the average becomes 25. The excluded number is | [
"25",
"27",
"30",
"37",
"40"
] | Sol.
Therefore excluded number
= (27 × 6) - ( 25 × 5)
= 162 – 125
= 37.
Answer D
The answer is: D | D |
mathematics | The timing of a college is from 11 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. | [
"56 minutes",
"52 minutes",
"30 minutes",
"48 minutes",
"44 minutes"
] | Explanation:
Total time a student spends in college = 5 hours 20 minutes = 280 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (280 – 20)/5
= 52 minutes
ANSWER B
The answer is: B | B |
mathematics | Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 570 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Fredd... | [
"8/3",
"3/8",
"38/15",
"5/8",
"5/3"
] | Distance traveled by Eddy = 570 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 570/3 = 190 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 190/75 = 38/15
Answer C
The answer is: C | C |
mathematics | The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January? | [
"3999",
"7867",
"4500",
"2789",
"3671"
] | Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2)
(2)-(1) i.e. May - Jan = 2000
Salary of May is Rs.6500
Salary of January
= Rs.4500
Answer: C
The... | C |
mathematics | A and B walk around a circular track. They start at 1 p.m from the same point in the opposite directions. A and B walk at a speed of 4 rounds per hour and 6 rounds per hour respectively. How many times shall they cross each other before 4 p.m | [
"15",
"20",
"25",
"30",
"35"
] | Explanation:
Relative speed = (4+6) =10 rounds per hour
So, they cross each other 30 times in three hours hence, they cross 30 times before 4 p.m
Answer: Option D
The answer is: D | D |
mathematics | The perimeter of a rhombus are 24 cm and 10 cm, the area and the perimeter of the rhombus is | [
"64 sq.m",
"70 sq.m",
"78 sq.m",
"84 sq.m",
"None"
] | Solution
Perimeter of the rhombus = 56 m
Each side of the rhombus = 56 / 4 m
= 14 m.
Height of the rhombus = 5 m
Area = (14 x 5) m²
= 70 m²
Answer B
The answer is: B | B |
mathematics | On a store counter are exactly two boxes containing only purple marbles and yellow marbles. Box A has 30 purple marbles and 20 yellow marbles; box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one of the boxes and then randomly selects one marble from the box, what is the probability that t... | [
"3/20",
"3/10",
"9/20",
"3/5",
"9/10"
] | The question asks us to select a purple marble from either of the boxes. Here we need to select a box first(either A or B) and then select the marble from the box. So these events are AND events i.e. both need to be done to select a purple marble from the box. For an AND event we multiply the probability of the events.... | C |
mathematics | In a business A and C invested amounts in the ratio 2 : 1. Whereas the ratio between amounts invested by A and B was 3 : 2. If 1,57,300 was their profit, how much amount did B receive? | [
"72,600",
"48,400",
"36,300",
"24,200",
"None of these"
] | Ratio A : B = 3 : 2 and A : C = 2 : 1
\ A : B : C = 6 : 4 : 3
Profit share of B = 4 × 1,57,300 = 48400
Answer B
The answer is: B | B |
mathematics | The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 6hrs if the speed of the bike is twice speed of the tractor? | [
"400 km",
"500 km",
"360 km",
"540 km",
"600 km"
] | Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 6 h is
90 × 6 = 540 km
Ans.(D)
The answer is: D | D |
mathematics | How many positive factors do 120 and 80 have in common? | [
"8",
"12",
"16",
"18",
"24"
] | The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 120 and 80 is 40
Number of factors of 40 = 8
Answer :A
The answer is: A | A |
mathematics | Two bus tickets from city A to B and three tickets from city A to C cost Rs. 385 but three tickets from city A to B and two tickets from city A to C cost Rs. 365. What are the fares for cities B and C from A ? | [
"s. 4, Rs. 23",
"s. 13, Rs. 17",
"s. 15, Rs. 14",
"s. 17, Rs. 13",
"s. 65, Rs. 85"
] | If fares for cities B and C from A are x and y respectively, then
2x+3y=385 or 6x+9y= 1155
3x+2y =365 or 6x+4y= 730
subtracting
5y = 425
y= Rs 85
Hence E. Rs. 65, Rs. 85
ANSWER:E
The answer is: E | E |
mathematics | In a series of consecutive numbers, 27 is the eighth smallest number and 20 is the tenth largest number. What is the range of the series? | [
"32",
"30",
"28",
"16",
"25"
] | Imp:All are consecutive odd numbers.
27 is the 8th smallest ,there are 7 numbers smaller then 27 ,smallest number :27-14=13
20 is the 10th largest ,so there are 9 numbers larger then 20, largest number:20+18=38
Range:38-13=25
Ans : E
The answer is: E | E |
mathematics | The average salary of all the employees in a small company is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of employees in the company is: | [
"20",
"21",
"22",
"23",
"24"
] | Explanation :
Let the total number of employees be x. then,
8000x = (12000 x 7) + 6000 (x 7)
2000x = 42000
x = 21.
Answer : B
The answer is: B | B |
mathematics | From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 7, what is the probability that the 2 numbers included the number 5? | [
"1/5",
"2/5",
"3/10",
"3/5",
"1/3"
] | We know that the sum of two numbers picked was 7. So, there could be the following cases:
(1, 6);
(6, 1);
(2, 5);
(5, 2);
(3, 4);
(4, 3);
Total of 6 cases out of which 2 have 5, thus the probability is 2/6=1/3.
Ans E
The answer is: E | E |
mathematics | In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 4% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year? | [
"1 : 2",
"5 : 4",
"2 : 3",
"Data inadequate",
"None of these"
] | Let the population of males = x; then the population of females = 9000 – x
Now, 4% of x + 8% of (9000 – x)
= (9600 – 9000 ) = 600
or 0.04x + 720 – 0.08x = 600
or 720 – 600 = 0.08x – 0.04x
or, 120 = 0.04x
x = 3000
Reqd ratio of population of males and females
3000/9000−3000=3000/6000=1:2
Answer A
The answer is: A | A |
mathematics | 800 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? | [
"a) 162",
"b) 138",
"c) 16",
"d) 38",
"e) 12"
] | Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 800 = 16
Answer: C
The answer is: C | C |
mathematics | If a and b are positive integers and b ≠ 1, then ab(b −1) is | [
"ab^2-ab",
"2/b",
"1/b",
"1/a",
"1/a+1/b"
] | Answer : A
The answer is: A | A |
mathematics | A shopkeeper sold a TV set for 17940, at a discount of 8 % and gained 19.6 %.If no discount is allowed, what will be his gain per cent? | [
"25 %",
"36.4 %",
"24.8 %",
"Can’t be determined",
"None of these"
] | If no discount is given,selling price of TV
= 17940 × 100⁄92 = 19500
Cost price of TV = 17940×100/119.60x15000
Gain % = 19500−15000/15000×100= 30 %
Answer E
The answer is: E | E |
mathematics | A MAN wants to plant trees in his garden in rows in such a way that the number of trees in each row to be the same. If there are 12 rows the number of trees in each row is 24 if there are 6 more rows find the number of trees in each row? | [
"A)63",
"B)8",
"C)48",
"D)32",
"E)33"
] | Required number of trees
= 12/36 * 24= 8.
ANSWER:B
The answer is: B | B |
mathematics | A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. | [
"150 meter",
"286 meter",
"186 meter",
"288 meter",
"265 meter"
] | Speed = 60*(5/18) m/sec
= 50/3 m/sec
Length of Train (Distance)
= Speed * Time
(50/3) * 9 = 150 meter
Answer:A
The answer is: A | A |
mathematics | A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 245, then how much amount should C pay as his share of rent? | [
"35",
"45",
"25",
"63",
"55"
] | A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=245×9/35=7×9=63
Answer is D
The answer is: D | D |
mathematics | A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is: | [
"65 kg",
"62 kg",
"120 kg",
"60 kg",
"50 kg"
] | Volume of water displaced = (3 x 2 x 0.01) m3
= 0.06 m3.
Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.
ANSWER D
The answer is: D | D |
mathematics | Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in five hours, what fraction of the room can Joseph paint in 20 minutes? | [
"1/5x",
"x/(x-3)",
"(x-5)/15x",
"x/(x-5)",
"(x-5)/x"
] | Let J be Joseph's rate per hour.
1/x + J = 1/5 of a room per hour
J = 1/5 - 1/x, of a room per hour
In 20 minutes, Joseph can paint 1/3*(1/5-1/x) = 1/15-1/3x = (x-5)/15x
The answer is C.
The answer is: C | C |
mathematics | If two numbers are in the ratio 2:3. If 7 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number? | [
"A)12",
"B)14",
"C)20",
"D)24",
"E)26"
] | 2:3
2x + 7 : 3x + 7 = 3 : 4
4[2x + 7] = 3[3x + 7]
8x + 28 = 9x + 21
9x - 8x = 28 - 21
x = 7
Then smallest number is = 2
2x = 14
Correct Option B
The answer is: B | 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 9 minutes. The waste pipe can empty the full cistern in? | [
"18",
"17",
"16",
"19",
"15"
] | 1/10 + 1/15 - 1/x = 1/9
x = 18
Answer:A
The answer is: A | A |
mathematics | Using all the letters of the word "BETA", how many words can be formed, which begin with B and end with A? | [
"5",
"6",
"8",
"9",
"2"
] | There are five letters in the given word.
Consider 4 blanks ....
The first blank and last blank must be filled with B and A all the remaining three blanks can be filled with the remaining 2 letters in 2! ways.
The number of words = 2! = 2.
Answer: E
The answer is: E | E |
mathematics | A mail handler needs 3 hours to sort the mail. His assistant takes 6 hours to sort the mail. How many hours will it take for both of them working together to sort the mail? | [
"3",
"2",
"1",
"2 1/2",
"1 1/5"
] | Work hrs=AB/(A+B)= 18/9 =2
Answer is B
The answer is: B | B |
mathematics | The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is? | [
"3",
"4",
"9",
"3",
"5"
] | Explanation:
P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.
Answer: Option B
The answer is: B | B |
mathematics | Ram's salary is 25% more than Raja's. How much percent is Raja's salary less than Ram's? | [
"10%",
"15%",
"20%",
"25%",
"50%"
] | Raja's salary less than Ram's by 25/(100+25) * 100% = 20%
Answer is C
The answer is: C | C |
mathematics | Curious Elva asked her father what he would gift for her nineteenth birthday. Father replied that it would depend on the day of the week and be one of SUNglasses, MONeybag, ..., FRIedcake, and SATchel. Please help Elva find the day of the week on 08-Jan-2029 | [
"Monday",
"Tuesday",
"Thursday",
"Saturday",
"Sunday"
] | at year 2000 there is 0 odd day as it is multiple of 400.
from 2001 to 2028 there are 28 years in which 28/4 = 7 are leap years and 21 are ordinary days.
Odd day in 7 leap years = 7*2 = 14
Odd day in 21 ordinary days = 21
total odd day till 31 dec 2028 = 14+21 = 35/7 = 0
hence 1jan 2029 will be Monday.
&
8jan 2029 will... | A |
mathematics | A batsman scored 100 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets? | [
"50%",
"40%",
"60%",
"70%",
"80%"
] | Number of runs made by running = 100 - (3 x 4 + 8 x 6)
= 100 - (60)
= 40
Now, we need to calculate 40 is what percent of 100.
=> 40/100 x 100 = 40 %
ANSWER:B
The answer is: B | B |
mathematics | In a forest 250 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in ... | [
"150",
"750",
"1,250",
"1,500",
"2,500"
] | The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 250 tagged deers comprise 10% of total # of deers --> total # of deers =250*10 = 2,500.
Answer: E
The answer is: E | E |
mathematics | The simple interest in 14 months on a certain sum at the rate of 6 per cent per annum is 250 more than the interest on the same sum at the rate of 8 per cent in 8 months. How much amount was borrowed? | [
"15000",
"25000",
"7500",
"14500",
"None of these"
] | Let the amount be x.
From the question, x×14×6/1200−x×8×8/1200=250
∴ x = 15000
Answer A
The answer is: A | A |
mathematics | The G.C.D. of 1.08, 0.36 and 0.6 is? | [
"0.03",
"0.9",
"0.18",
"0.12",
"none of these"
] | Given numbers are 1.08,0.36 and 0.60.
H.C.F of 108, 36 and 60 is 12
H.C.F of given numbers=0.12.
Correct Options:D
The answer is: D | D |
mathematics | 5 girls and 3 boys are arranged randomly in a row. Find the probability that:
1) there is one boy on each end.
2) There is one girl on each end. | [
"3/28 & 5/14",
"5/28 & 3/14",
"5/14 & 3/28",
"3/28 & 1/14",
"1/28 & 5/14"
] | Total # of arrangements is 8!;
1. The # of arrangements where there is one boy on each end is C^2/3∗2∗6! where C^2/3C32 is # of ways to select which 2 boys will be on that positions, *2 # of way to arrange them on that position (A------B and B------A) and 6! is # of arrangements of 6 people left;
P=C^2/3∗2∗6!/8!=3/28
2... | A |
mathematics | A is the average (arithmetic mean) of the first 7 positive multiples of 6 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n? | [
"8",
"10",
"12",
"16",
"24"
] | If A^2 - B^2 = 0, then let's assume that A = B.
A must equal the 4th positive multiple of 4, thus A = 24, which also equals B.
B is the second positive multiple of n, thus n = 24/2 = 12.
The answer is C.
The answer is: C | C |
mathematics | On dividing 23 by a number, the quotient is 5 and the remainder is 3. Find the divisor. | [
"1",
"2",
"4",
"6",
"7"
] | d = (D-R)/Q
= (23 - 3)/5
= 20/5 = 4
C
The answer is: C | C |
mathematics | Find the invalid no.from the following series 13, 18, 25, 30, 37, 40 | [
"13",
"18",
"40",
"37",
"40"
] | The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C
The answer is: C | C |
mathematics | The simple interest on Rs.12000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for five years at the same rate of interest. | [
"3052.82",
"3052.89",
"3052.85",
"3052.8",
"3052.82"
] | R = 100 I / PT
=> R = (100 * 7200)/ (12000 * 5) = 12%
CI = P{ [1 + R /100]n - 1}
= 12000 { [ 1 + 12 / 100]2 - 1} = Rs.3052.80
Answer:D
Answer:D
The answer is: D | D |
mathematics | If 4 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is? | [
"10:5:5",
"10:5:8",
"10:5:2",
"10:5:4",
"10:5:1"
] | 4A = 8B = 10 C
A:B:C = 1/4:1/8:1/10
= 10:5:4
Answer: D
The answer is: D | D |
mathematics | Find the middle one when The sum of five consecutive even numbers is 65? | [
"9",
"13",
"15",
"17",
"11"
] | Let the first number be n
Let the second number be n + 2
Let the third number be n + 4
Let the third number be n + 6
Let the third number be n + 8
n + n + 2 + n + 4 + n + 6 + n + 8= 65
Combine like terms:
5n + 20 = 65
5n = 65 - 20
5n = 45
5n = 45
n = 9
n + 2 = 11
n + 4 = 13
n + 6 = 15
n + 8 = 17
The middle number is 13... | B |
mathematics | 12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 9. | [
"150",
"162",
"154",
"158",
"144"
] | D = d * Q + R
D = 17 * 9 + 9
D = 153 + 9
D = 162
ANSWER B
The answer is: B | B |
mathematics | Together, Andrea and Brian weigh p pounds; Brian weighs 12 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds? | [
"p/2 - 10",
"3p/4 - 6",
"3p/2 - 5",
"5p/4 - 10",
"5p - 5"
] | Together, Andrea and Brian weigh p pounds --> A + B = p.
Brian weighs 10 pounds more than Andrea --> B = A + 12 --> A + (A + 12) = p --> A = (p - 12)/2 = p/2 - 6.
Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 6) + p/4 = 3p/4 -6.
Answer: B.
The answer is: B | B |
mathematics | A student traveled 30 percent of the distance of the trip alone, continued another 40 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip? | [
"120",
"140",
"160",
"180",
"200"
] | Let x be the total length of the trip.
0.3x + 40 miles + 0.5x = x
40 miles = 0.2x
x = 200 miles
The answer is E.
The answer is: E | E |
mathematics | In the xy-coordinate system, line k passes through points (-9m, 0) and (0, 3m). Which of the following is a possible equation of line k? | [
"y = -3x + 3m",
"y = 1/3*x - 9m",
"y = 3x + 3m",
"y = 1/3*x + 3m",
"y = -1/3*x - 9m"
] | The slope of the line is 3m/9m=1/3.
The y-intercept is 3m.
the equation of the line is: y = 1/3*x +3m
The answer is D.
The answer is: D | D |
mathematics | The number of timeshare condos available at Sunset Beach is 3/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 320, what is the difference between the number of condos available at Sunset Beach and the number of condos availabl... | [
"80",
"90",
"120",
"150",
"240"
] | Let x be the number of timeshare condos available at Playa del Mar.
Then number of timeshare condos available at Sunset Beach = 3/5x
We know, x + 3/5 x = 320
Hence, x = 200. So, number of timeshare condos available at Playa del Mar = 200
the difference between the number of condos available at Sunset Beach and the numb... | A |
mathematics | If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is | [
"12 kmph",
"13 kmph",
"14 kmph",
"15 kmph",
"None of these"
] | Explanation:
Rate upstream = (7/42)*60 kmh = 10 kmph.
Speed of stream = 3 kmph.
Let speed in sttil water is x km/hr
Then, speed upstream = (x —3) km/hr.
x-3 = 10 or x = 13 kmph
Option B
The answer is: B | B |
mathematics | On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ? | [
"0",
"3",
"5",
"11",
"7"
] | Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
Required remainder = 5.
Answer :C
The answer is: C | C |
mathematics | A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? | [
"5.78",
"5.28",
"5.76",
"5.16",
"5.19"
] | M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer:C
The answer is: C | C |
mathematics | Two trains are moving in opposite directions with speed of 110 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds | [
"26",
"48",
"47",
"36",
"25"
] | Explanation:
Relative speed = 110+90 = 200 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/200 hr = 1/100 hr = 3600/100 = 36 seconds
Answer: Option D
The answer is: D | D |
mathematics | Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 70% of the previous term. What is the value range of the five numbers? | [
"7,599",
"9,750",
"9,975",
"9,984",
"10,736"
] | 1st number= 10,000
2nd number = 70% of 10,000= 7000
3rd number= 70% of 7000= 4900
4th number = 70% of 4900= 3430
5th number= 70% of 3430= 2401
Range = 10,000-2401=7599
A is the answer
The answer is: A | A |
mathematics | Which number is the odd one out?
159
642
693
537
289
582 | [
"916",
"345",
"895",
"642",
"624"
] | D
642
In the rest there is the same difference between each digit, eg: 6 (–2) 4 (–2)2
The answer is: D | D |
mathematics | A crate measures 7 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit... | [
"2",
"4",
"6",
"7",
"12"
] | We can find the radius of all the three cases of cylinders.
The only crux to find the answer faster is that:
Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.
So r=7 for the surface 8*12 face.
Volume = 343pi
Answer D
The answer is: D | D |
mathematics | Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical? | [
"25%",
"28.1%",
"20%",
"12.5%",
"11.1%"
] | Welcome, just post the question and the choices
Let's see, the way I did it was
1/3 are clerical out of 3600 so 1200 are clerical
1200 reduced by 1/4 is 1200*1/4
so it reduced 300 people , so there is 900 clerical people left
but since 300 people left, it also reduced from the total of 3600 so there are 3300 people tot... | B |
mathematics | The maximum number of students among them 640 pens and 520 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? | [
"40",
"45",
"50",
"55",
"60"
] | number of pens = 640
number of pencils = 520
Required number of students = H.C.F. of 640 and 520= 40
Answer is A
The answer is: A | A |
mathematics | Last year Elaine spent 20% of her annual earnings on rent. This year she earned 15% more than last year and she spent 25% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year? | [
"152.5",
"143.75",
"155.5",
"165.5",
"117.5"
] | For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.
She would've spent $20 of this on rent.
This year she earned 15% more, or $115.
She would've spent 25% of this on rent, or $28.75
Do $34.5/$20
This will give you 143.75%
B is the correct answer.
The answer is: ... | B |
mathematics | The greatest number of four digits which is divisible by 25, 36, 40 and 75 is: | [
"9000",
"9400",
"9600",
"9800",
"9200"
] | Greatest number of 4-digits is 9999.
L.C.M. of 25, 36, 40 and 75 is 1800.
On dividing 9999 by 1800, the remainder is 999.
Required number (9999 - 999) = 9000.
Answer: Option A
The answer is: A | A |
mathematics | Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years? | [
"30",
"25",
"24",
"35",
"40"
] | Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.
ANSWER C
The answer is: C | C |
mathematics | What is the sum of the first 25 natural numbers (starting from 1)? | [
"325",
"350",
"375",
"400",
"425"
] | The sum of n natural numbers = n*(n+1) / 2 = 25*26/2 = 325
The answer is A.
The answer is: A | A |
mathematics | Which of the following is the best approximation for y?
1/2−1/3+1/6−1/10+1/12−1/14+1/16 | [
"0.1",
"0.31",
"0.35",
"0.4",
"0.6"
] | 1/2 - 1/3 +1/6-1/10+1/12-1/14+1/16
=> 1/2 [1+1/3-1/5+1/6-1/7+1/8] - 1/3
=> 0.5 [ 1+0.33-0.2+0.167-0.142+0.125] - 0.33
=> 0.31
Option B
The answer is: B | B |
mathematics | If a and b are integers and (a*b)^5 = 48y, y could be: | [
"8",
"16",
"162",
"144",
"100"
] | Distribute the exponent.
a^5 * b^5 = 48 y
Find the prime factorization of 48. This is 2^4 *3^1.
We need 2^1*3^4 (or some other power of 3 that will give us a multiple of 3^5 as our second term).
3^4*2 = 81*2= 162
The answer is C.
The answer is: C | C |
mathematics | There are 44 students in a hostel, due to the administration, 15 new students has joined. The expense of the mess increase by Rs. 33 per day. While the average expenditure per head diminished by Rs. 3, what was the original expenditure of the mess ? | [
"Rs. 618",
"Rs. 612",
"Rs. 622",
"Rs. 616",
"Rs. 630"
] | Explanation:
Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(... | D |
mathematics | A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? | [
"5",
"4",
"6",
"7",
"8"
] | 7 * 8 : 9 * x = 8:9 => x= 7
Answer:D
The answer is: D | D |
mathematics | For every $20 that a billionaire spends, a millionaire spends the equivalent of 10 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as | [
"1 : 4 : 400",
"1 : 4 : 100",
"20 : 4 : 1",
"1:4:800",
"400 : 4 : 1"
] | millionaire 10 cents = 1/10 dollar ..therefore 1 dollar M = 200 dollar of B
therefore 4 dollar M = 800 dollar of B also 1 dollar Y
Y:M:B = 1:4:800
= 1:4:800
D
The answer is: D | D |
mathematics | daal is now being sold at rate Rs.20 a kg.During last month its rate was Rs 16 per kg.By How reduce percent should a family its consumption so as to keep the expenditure fixed? | [
"10%",
"20%",
"30%",
"40%",
"50%"
] | Last month rate= 16 per kg
this month rate = 20 per kg
if 20=100% then 16= ?
therefore %= (16 * 100)/20=80%
to reduce consumption 100-80=20%
ANSWER:B
The answer is: B | B |
mathematics | In one hour, a boat goes 6 km along the stream and 2 km against the stream. the sped of the boat in still water (in km/hr) is : | [
"4",
"5",
"8",
"9",
"10"
] | Solution
Speed in still water= 1/2(6+2) km/hr= 4kmph. Answer A
The answer is: A | A |
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