subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 28 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cycli... | [
"6 2/3",
"15",
"20",
"25",
"30"
] | Here is how I did it:
The cyclist travels 28 miles in 60 mins, so in 5 mins he will travel [(28*5)/60] miles, which equals 7/3 miles in 5 mins.
Now the hiker travels 4 miles in 60 mins. To travel 7/3 miles, he will take [(60*7/3)/4] = 35 mins.
hence 35-5 =30 mins
E
The answer is: E | E |
mathematics | Find the least number of 5 digits, which is exactly divisible by 89. | [
"27",
"37",
"932",
"12",
"91"
] | ANSWER:A
The answer is: A | A |
mathematics | Solve the given two equations and find the inequality of X and Y. (a) x^2-1=0 and (b) y^2+4y+3=0 | [
"If x>y",
"If x>=y",
"If x < y",
"If x<=y",
"x=y or relationship cannot be established"
] | Solution:-
X=+1,-1 and Y= -1,-3
Comparing we get X>=Y
B
The answer is: B | B |
mathematics | A university cafeteria offers 4 flavors of pizza - pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ? | [
"4",
"8",
"12",
"16",
"32"
] | There are 4 flavors of pizza and each can be:
1. Without cheese and mushrooms;
2. With cheese;
3. With mushrooms;
4. With cheese and mushrooms.
So, the total number of pizza varieties is 4*4 = 16.
Answer: D.
The answer is: D | D |
mathematics | There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.? | [
"r / (r + b + w)",
"r / (r + b)",
"(r + b + w)/r",
"r / (b + w)",
"r * (r + b + w)"
] | The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
A
The answer is: A | A |
mathematics | If 15,555 β n is divisible by 11, and 0 < n < 11, what is n? | [
"1",
"3",
"5",
"7",
"9"
] | 15,555 / 11 = 1414 with a remainder of 1.
We need to subtract the remainder to get a multiple of 11.
The answer is A.
The answer is: A | A |
mathematics | Ms. Lovely deposits $ 300 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year? | [
"$118.00",
"$120.00",
"$121.00",
"$122.00",
"$140.00"
] | Using Formula - A = P(1+r/n)^nt
Given
P=300
n=2
t=1
r=0.2
Substituting value in formula
A = 300(1+0.2/2)^2
A= 363.00$=C
The answer is: C | C |
mathematics | Which of the following fractions T, if written as a decimal, would have a 2 in the thousandths place ? | [
"3/11",
"7/9",
"1/8",
"4/7",
"1/6"
] | (A) T=3/11 = 0.2727272727....
Answer: A
The answer is: A | A |
mathematics | A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? | [
"500bc",
"500b/c",
"1000bc",
"1000b/c",
"1000/bc"
] | 2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips
The answer is C.
The answer is: C | C |
mathematics | A can do a piece of work 40 days. B can do work in 60 days. In how many days they will complete the work together? | [
"15 days",
"16 days",
"19 days",
"17 days",
"24 days"
] | LCM = 120, Ratio= 40:60=2:3
No of days= 120/(2 + 3) = 90/5 = 24 days
ANSWER:E
The answer is: E | E |
mathematics | What is the 56743rd term in the series 1234567891011121314β¦β¦.? | [
"1",
"3",
"7",
"5",
"6"
] | 1 to 9=9 no.s 1 digit each no.
9 to 99=90no.s 2 digit each,total digit=90*2=180 terms
99 to 999=900 no.s 3 digit each,total digit=900*3=2700
999 to 9999=9000 no.s 4 digit each,total digit=9000*4=36,000
now till 999,we have=9+180+2700=2889 digits
till 9999 we hv=2889+36000=38889 digits
56743-38889=17854
after 9999 each ... | C |
mathematics | Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? | [
"9",
"8",
"7",
"6",
"4"
] | Explanation:
x β y = 5
4x β 6y = 6
x = 12 y = 7
Answer: Option C
The answer is: C | C |
mathematics | Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? | [
"22",
"37",
"10",
"28",
"27"
] | speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distancespeed=954 hour=16 hour = 606 min=10 min
An... | C |
mathematics | A bag contains 25 paise, 50 paise and 1 rupee coins in the ratio 7:4:3 . total no. of coins is 360. sum of total coins is Rs. 99 so how many 25 paise coins? | [
"160",
"170",
"180",
"190",
"200"
] | total coins=360
25 p coins =(7/14)*360=180
ANSWER:C
The answer is: C | C |
mathematics | The length and breadth of a rectangle is increased by 10% and 30% respectively. What is the increase in the area? | [
"43.0",
"44.0",
"43.5",
"45.0",
"42.0"
] | 100*100=10000
110*130=14300
----------
4300
10000-------4300
100-------43.00
Answer A
The answer is: A | A |
mathematics | What number would replace the question mark in this quite difficult number sequence ?
21 32 54 87 131 ? | [
"300",
"125",
"450",
"340",
"186"
] | E
186
Explanation :
21+11*1 => 32
32+11*2 => 54
54+11*3 => 87
87+11*4 => 131
131+11*5 => 186
The answer is: E | E |
mathematics | A professional stock trader just signed her new yearly contract with her employer. She will receive a 6% raise over last year's pay for her base pay, plus the chance to earn a performance bonus of up to $3,000. Last year, she earned no performance bonus. This year, assuming that she earns the full performance bonus, he... | [
"162,000",
"173,000",
"180,000",
"213,000",
"284,000"
] | let x = last year's pay
this year's pay + 3,000 = this year's effective pay
(1+.06)*x + 3,000 = (1+.08)*x
1.06x + 3,000 = 1.08x
3,000 = .02x
150,000 = x
thus the new pay effectively is (1+.08)*150,000 = 162,000
A
The answer is: A | A |
mathematics | The number 50 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3? | [
"2",
"5",
"7",
"8",
"9"
] | Notice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-3,+/-4and +/-5, so the difference could be 2,-2 or 1. Since only one of them is among the choices, then it must be the correct answer.
Answer: A
The answer is: A | A |
mathematics | complete the numerical series with the correct number
5+3+1=15517
9+2+2=181834
5+6+4=302044
5+4+2=201026
9+3+5= ? | [
"468645",
"454586",
"274569",
"454386",
"444586"
] | 9+3+5= 274569
Answer : C
The answer is: C | C |
mathematics | A vendor bough toffees at 6 for a rupee. how many for a rupee must he sell to gain 20%? | [
"3",
"8",
"5",
"9",
"1"
] | C.P or toffees = Rs.1, S.P of 6 toffee = 120% of Rs.1 = Rs.6/5
for Rs. 6/5, toffees sold=6, for Rs.1, toffees sold= (6*5/6)= 5
Correct answer (C)
The answer is: C | C |
mathematics | What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually? | [
"Rs.9688",
"Rs.9687",
"Rs.3338",
"Rs.9632",
"Rs.9680"
] | Explanation:
A= P{1 + R/100}n
=> 8000{1 + 10/100}2 = Rs.9680
Answer: E
The answer is: E | E |
mathematics | 5358 x 51 = ? | [
"272258",
"272358",
"273258",
"274258",
"274358"
] | 5358 x 51 = 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
C)
The answer is: C | C |
mathematics | A life insurance company insured 25,000 young boys, 14,000 young girls and 16,000 young adults. The probability of death within 10 years of a young boy, young girl and a young adult are 0.02, 0.03 and 0.15 respectively. One insured person dies. What is the probability that the dead person is a young boy? | [
"36/165",
"25/166",
"26/165",
"32/165",
"33/165"
] | The number of young boys that will die = 0.02 x 25,000 = 500
The number of young girls that will die = 0.03 x 14,000 = 420
The number of young adults that will die = 0.15 x 16,000 = 2400
The required probability = The number of young boys who will die / The total number of people who will die.
= 500 / (500 + 420 + 2400... | B |
mathematics | The average of first five multiples of 7 is: | [
"9",
"16",
"15",
"8",
"21"
] | Explanation :
(7(1+2+3+4+5)/5
= 7x15/5
= 21
Answer : E
The answer is: E | E |
mathematics | What will come in place of the x in the following Number series? 2, 7, 10, 22, 18, 37, 26, x | [
"29",
"32",
"35",
"42",
"52"
] | There are two series here
2, 10, 18, 26, ... (Increase by 8)
7, 22, 37, ... (Increase by 15)
Hence, next term is 37+15 = 52
E
The answer is: E | E |
mathematics | The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275 , then the other is | [
"344",
"387",
"308",
"299",
"882"
] | Explanation:
other number = \inline \fn_jvn \left ( \frac{11\times 7700}{275} \right ) = 308
Answer: C) 308
The answer is: C | C |
mathematics | 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 18 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists t... | [
"A)11",
"B)18",
"C)24",
"D)29",
"D)36"
] | lets solve by creating equation..
W = 31..
Total = 50..
Not W = 50 -31= 19..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=19 or x=8..
so who won Nobel but not Wolf = x+3 = 11..
But people who won BOTH W and N = 13..
so total who won N = 11+18 = 29..
D
The answer is: D | D |
mathematics | Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made? | [
"16.5",
"12.5",
"14.5",
"12",
"13"
] | et the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) =... | A |
mathematics | In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 11 and 200, then the least and greatest integer on the card would be | [
"3 and 15",
"3 and 20",
"4 and 13",
"4 and 14",
"5 and 14"
] | Given: 11<x(x+1)<200.
Now, it's better to test the answer choices here rather than to solve:
If x=3 then x(x+1)=12>11 --> so, the least value is 4. Test for the largest value: if x=15 then
x(x+1)=15*16=240>200 --> discard B.
Answer: A.
The answer is: A | A |
mathematics | Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. | [
"$204",
"$231",
"$156",
"$145",
"$200"
] | Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
The answe... | D |
mathematics | Write 890,000,000,000 in scientific notation. | [
"8.9 * 10 11",
"800.900 * 10 11",
"8.900 * 10 11",
"80.9000* 10 11",
"08.900 * 10 11"
] | a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
890,000,000,000 = 8.9* 100,000,000,000 = 8.9 * 10 11**
correct answer A
The answer is: A | A |
mathematics | Marcella has 27 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left? | [
"22",
"20",
"19",
"16",
"15"
] | Marcella has 27 pairs of shoes and loses 9 shoes.
To minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes).
The 27 pairs of shoes minus the 5 'destroyed' pairs yields 22 pairs tha... | A |
mathematics | On my sister's 15th birthday, she was 159 cm in height, having grown 6% since the year before. How tall was she the previous year? | [
"150 cm",
"140 cm",
"142 cm",
"154 cm",
"None of these"
] | Explanation :
Given that height on 15th birthday = 159 cm and growth = 6%
Let the previous year height = x
Then height on 15th birthday = x Γ100+6/100=xΓ106/100
β159 = x Γ (106/100)
βοΏ½x=159Γ100/106=1.5Γ100=150;cm
Answer : Option A
The answer is: A | A |
mathematics | Each shelf of a bookcase contained 11 books. If the librarian took out 31 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 4 books, how many shelves does the bookcase have? | [
"5",
"6",
"7",
"8",
"9"
] | Let x be the number of shelves.
11x - 31 = 7(x-1) + 4
4x = 28
x = 7
The answer is C.
The answer is: C | C |
mathematics | A train 180 m long passed a pole in 3 sec. How long will it take to pass a platform 330 m long? | [
"5",
"6",
"7",
"8",
"9"
] | Speed = 180/3
= 60 m/sec.
Required time
= (180 + 300)/60
= 8 sec.
Answer:D
The answer is: D | D |
mathematics | Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? | [
"20 m",
"60 m",
"50 m",
"45 m",
"65 m"
] | Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
The answer is: B | B |
mathematics | (4300231)-?=2535618 | [
"1865113",
"1775123",
"1764613",
"1675123",
"None of them"
] | Let 4300231-x=2535618
then x=4300231-2535618
=1764613
Answer is C
The answer is: C | C |
mathematics | A boat goes 100 km downstream in 10 hours, and 60 m upstream in 15 hours. The speed of the stream is? | [
"3",
"22 1/4",
"22 1/2",
"22 1/1",
"22 1/3"
] | 100 --- 10 DS = 10
? ---- 1
60 ---- 15 US = 4
? ----- 1 S = (10 - 4)/2
= 3 kmp Answer: A
The answer is: A | A |
mathematics | The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $21? | [
"33",
"35",
"37",
"39",
"41"
] | $21 = 3 * $6 + $3
The number of doughnuts is 3*12 + 3 = 39
The answer is D.
The answer is: D | D |
mathematics | On a sum of money, the simple interest for 2 years is Rs. 325, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is | [
"15%",
"14.25%",
"9.23%",
"10.5%",
"11.5%"
] | Explanation:
The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
= (R Γβ SI)/(2 Γβ 100)
Difference between the compound interest and simple interest = 340 - 325 = 15
(R Γβ SI)/(2 Γβ 100) = 15
(R Γβ 325)/(2 Γβ 100) = 15
R = 9.23%
Answer: Option C
The answer is: C | C |
mathematics | Which of the following is the Highest Common Factor of 27, 81 and 54? | [
"8",
"9",
"6",
"14",
"12"
] | the Highest Common Factor is 9
Ans is :B
The answer is: B | B |
mathematics | The distance from Steve's house to work is 30 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work? | [
"5.",
"10.",
"14.",
"15",
"20."
] | Time is in the ratio 2:1 :: to: fro office
Therefore, 2x+1x=6 hrs
Time take to come back - 2 hrs, distance travelled - 30 km => Speed = 15 kmph
ANSWER:D
The answer is: D | D |
mathematics | What quadrants do the line y = 2x - 4 go through? | [
"1 and 2",
"1 and 3",
"1 and 4",
"1,2 and 3",
"1,3 and 4"
] | Find the x-intercept and the y-intercept of the line.
To find the x intercept, set y = 0 and solve for x.
0 = 2x - 4
x = 2
To find the y intercept, set x = 0 and solve for y.
y = 0 - 4
y = -4
Draw the line using the two intercepts.
Thus, the line goes through the 1st, 3rd and 4th quadrants.
Answer is E
The answer is: E | E |
mathematics | If x, y, and z are positive integers and x = 14y = 7z, then the least possible value of x + y + z is | [
"33",
"40",
"49",
"61",
"17"
] | x + y + z = x/14 + x + x/7
= (1 + 14 + 2 )x/14 = 17x/14
17 is not divisible by 14(it's a prime #), so for least value, x = 14
Answer -E
The answer is: E | E |
mathematics | Operation#is defined as adding a randomly selected two digit multiple of 4 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers? | [
"0%",
"10%",
"20%",
"30%",
"40%"
] | Any multiple of 4 is even.
Any two-digit prime number is odd.
(even+odd)/2 is not an integer. Thus # does not yield an integer at all.
Therefore P=0.
Answer: A.
The answer is: A | A |
mathematics | A sum of money at simple interest amounts to Rs. 1560 in 4 years and to Rs. 1590 in 6 years. The sum is: | [
"Rs. 1400",
"Rs. 1450",
"Rs. 1500",
"Rs. 1550",
"Rs. 1525"
] | S.I. for 2 years = Rs. (1590 - 1560) = Rs. 30.
S.I. for 4 years = Rs.(30 x 2) = Rs. 60.
Principal = Rs. (1560 - 60) = Rs. 1500.
Answer: Option C
The answer is: C | C |
mathematics | Look at this series: 55, 55, 40, 40, 25, 25, ... What number should come next? | [
"14",
"15",
"17",
"10",
"11"
] | In this series, each number is repeated, then 15 is subtracted to arrive at the next number.
The next number should be 10
Answer : D
The answer is: D | D |
mathematics | B @ K I 9 D ΓΒ© 5 2 T $ M 4 E J # U R 1 A ΓΒ΄ K 5 W 6 % F Q 7 H P 8 Z
How many such numbers are there in the above arrangement each of which is immediately followed by a symbol but not immediately preceded by a consonant? | [
"None",
"One",
"Two",
"Three",
"More than three"
] | Explanation:
Consonant Number Symbol
There is no such combination.
ANSWER IS A
The answer is: A | A |
mathematics | In an examination, a student scores 6 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 280 marks, the no of questions he attempts correctly is : | [
"A)20",
"B)38",
"C)90",
"D)88",
"E)37"
] | Let the number of correct answers be X.
Number of incorrect answers = (60 β X).
6x β (60 β x) = 280
=> 7x = 340
=> x = 20
Answer:A
The answer is: A | A |
mathematics | Two stations P and Q are 65 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet? | [
"9 am",
"12 am",
"10.30 am",
"12.30 am",
"11 am"
] | Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 65
=> 20x + 25(x-1) = 65
=> 45x = 90
=> x= 2
Means, they meet after 2 hours after 7 am, ie, they meet at 9 am
Answer is A.
Th... | A |
mathematics | Which of the following is not a prime number ? | [
"502",
"503",
"509",
"521",
"523"
] | Clearly, 502 is not a prime number.
Answer : A
The answer is: A | A |
mathematics | xy=1 then what is (3^(x+y)^2) / (3^(x-y)^2) | [
"81",
"4",
"8",
"16",
"32"
] | (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
3^4 = 81
Answer A
The answer is: A | A |
mathematics | The number N is 5,3H7, where H represents the ten's digit. If N is divisible by 9, what is the value of H? | [
"4",
"3",
"5",
"8",
"2"
] | If the number is divisible by 9, it must also be divisible by 3. Only 3 yields such a number.
Answer: B
The answer is: B | B |
mathematics | Worker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both A and B, working together to do same job. | [
"4/9",
"2 4/9",
"3 4/9",
"4 4/9",
"None of these"
] | Explanation:
In this type of questions, first we need to calculate 1 hours work, then their collective work as,
A's 1 hour work is 1/8
B's 1 hour work is 1/10
(A+B)'s 1 hour work = 1/8 + 1/10
= 9/40
So both will finish the work in 40/9 hours
=
4 4/9
Option D
The answer is: D | D |
mathematics | On Monday, Lou drives his vehicle with 26-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his vehicle to 32-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou's tires make per... | [
"Decrease by 14.3%",
"Decrease by 19%",
"Increase by 14.3%",
"Increase by 12.5%",
"Cannot be determined with the given information."
] | 416 is the LCM
On Tuesday 416/32 =13
On Monday 416/26 = 16
Therefore, 13-16/16 = -1/5=-19% decrease
Answer is B
The answer is: B | B |
mathematics | Two pipes A and B can fill a cistern in 37 Β½ min and 45 minutes respectively. Both the pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after | [
"6 minutes",
"9 minutes",
"45 minutes",
"3 minutes",
"4 minutes"
] | If pipe B is turned off after x mins, then
(2*30)/75 + x/45 =1
x/45 = 1-60/75 = 1/5
x= 45/5= 9 mins
ANSWER:B
The answer is: B | B |
mathematics | If Γ’β¬ΛKARNATAKAΓ’β¬β’ is coded as Γ’β¬ΛBAIEABABAΓ’β¬β’, then Γ’β¬ΛBIHARΓ’β¬β’ is coded as | [
"BARHI",
"BHARI",
"BHIAR",
"BIHAI",
"BIHAR"
] | M=13,1+3=4=D
A=1=A
SIMILARLY,
B=2=B
I=9=I
H=8=H
A=1=A
R=18=1+8=9=I
SO ANS IS
BIHAI
ANSWER:D
The answer is: D | D |
mathematics | Last year, the taxes for small enterprises, was a minimum of 28 dollars for every 5000 dollars of revenue. Tax rates were revised this year to a minimum tax of 2.5 dollars for every 1500 dollars of revenue. By approximately what percent did the ratio of tax to revenue decrease from the previous charge? | [
"70",
"69",
"71",
"66",
"72"
] | Initial tax/revenue ratio = 28/5000 = 84/15000
Revised charge/transaction ratio = 2.5/1500 = 25/15000
Answer: A
The answer is: A | A |
mathematics | The average weight of 8 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person? | [
"76 kg",
"77 kg",
"76.5 kg",
"Data inadequate",
"None of these"
] | total weight increases = 8 Γ 1.5 = 12 kg
so the weight of new person = 65 + 12 = 77 kg
Answer B
The answer is: B | B |
mathematics | A man invested Rs.1552 in a stock at 97 to obtain an income of Rs.128. What is the dividend from the stock? | [
"4",
"8",
"6",
"10",
"12"
] | By investing Rs.1552, income = Rs.128
By investing Rs.97, income = 128Γ97/1552=8
ie, dividend = 8%
Answer is B.
The answer is: B | B |
mathematics | For what values of k will the pair of equations 3x + 4y = 12 and (kx + 12y)/2 = 15 does not have a unique solution? | [
"12",
"9",
"3",
"7.5",
"2.5"
] | we have 2 equations
1. 3x + 4y = 12 -- > 9x + 12y = 36
2. (kx + 12y)/2 = 15 --> kx + 12y = 30
substract 1-2, we get (9-K)x = 6
i.e. x = 6/(9-k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B
The answer is: B | B |
mathematics | A computer manufacturer produces a certain electronic component at a cost of $100 per component. Shipping costs for delivering the components are $2 per unit. Further, the manufacturer has costs of $10,000 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and s... | [
"122",
"112",
"134",
"108",
"101"
] | $10000 is a fixed cost
Each component is $102 ($100 to produce, $2 to ship)
Manufacturer will be producing and selling 1000 components
so therefore the equation to find price would be
1000*p = 10000+(1000*100)+(1000*2)
p = (10000+100000+2000)/1000
p = 112
Answer: B
The answer is: B | B |
mathematics | A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? | [
"20 hours",
"25 hours",
"35 hours",
"Cannot be determined",
"None of these"
] | If c takes x hrs, B takes 2x hrs and A takes 4x hrs,
then
1/x +1/2x = 1/4x = 1/5
7/4x = 1/5
x= 7*5/4 hrs = 35/4 hrs
So A alone will take 4*35/4 = 35 hrs
ANSWER:C
The answer is: C | C |
mathematics | Which of the following values is the greatest | [
"a) 11% of 89",
"b) 22% of 78",
"c) 50% of 67",
"d) 44% of 56",
"e) 55% of 45"
] | Are you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says C
The answer is: C | C |
mathematics | The H.C.F. of two numbers is 25 and the other two factors of their L.C.M. are 14 and 16. The larger of the two numbers is | [
"276",
"299",
"312",
"400",
"None"
] | Solution
Clearly, the numbers are (25 x 14) and (25 x 16).
Larger number = (25 x 16) = 400.
Answer D
The answer is: D | D |
mathematics | 80 x 100 + 80 x 11 = ? | [
"7500",
"8880",
"6200",
"5200",
"None of them"
] | =80 x (100+11) (by distributive law)
=80 x 111
=8880
Answer is B
The answer is: B | B |
mathematics | At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering? | [
"404",
"452",
"444",
"468",
"422"
] | 312 + 222 - 112 (since 112 is counted twice )= 422
E is the answer
The answer is: E | E |
mathematics | 895.7 β 573.07 β 95.007 = ? | [
"227.623",
"224.777",
"233.523",
"414.637",
"None of these"
] | Solution
Given expression = 895.7 - (573.07 + 95.007) = 895.7 - 668.077 = 227.623. Answer A
The answer is: A | A |
mathematics | If p^3 is divisible by 80, then the positive integer p must have at least how many distinct factors? | [
"2",
"3",
"6",
"8",
"10"
] | Let say p = 10, checking divisibility by 80
10β10β10/80=25/2
Numerator falling short of 2
So, lets say p = 20, again checking divisibility by 80
20β20β20/80=100
20 is the least value of p for which p3 can be completely divided by 80
There are 6 distinct factors of 20 >> 1, 2, 4, 5, 10, 20
Answer = C
The answer is: C | C |
mathematics | a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five
numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of
the following numbers S was deleted? | [
"a",
"b",
"c",
"d",
"e"
] | a+b+c+d+e => 1+2+3+4+5=15
S=20%*15= 3 =>C
The answer is: C | C |
mathematics | A man invests some money partly in 12% stock at 108 and partly in 10% stock at 60.To obtain equal dividends from both,he must invest the money in the ratio : | [
"3 : 4",
"3 : 2",
"4 : 5",
"16 : 15",
"None"
] | Solution
For an income of Rs. 1 in 12% stock at 108, investment = Rs. (108/12)= Rs. 9 .
For an income of Rs. 1 in 10% stock at 60, investment = Rs.(60/10) = Rs. 6.
β΄ Ratio of investments = 9 :6 =3:2
Answer B
The answer is: B | B |
mathematics | The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? | [
"Rs. 2400",
"Rs. 2200",
"Rs. 2300",
"Rs. 2500",
"Rs. 2600"
] | Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore... | A |
mathematics | The compound interest on a certain sum for 2 years at 10% per annum is $525. The simple interest on the same sum for double the time at half the rate percent per annum is: | [
"$400",
"$500",
"$600",
"$800",
"$900"
] | Let the sum be $. P.
Then,[P(1+10/100)^2 - P] = 525
->P[(11/10)^2 - 1] = 525
P = (525*100/21) = 2500
SUM = $2500
SO SI = $(2500*5*4/100) = $ 500
ANSWER : B $500
The answer is: B | B |
mathematics | How many two-element subsets of <1, 2,3,4,5,6,7,8> are there that do not contain the pair of elements 2 and 4? | [
"11",
"22",
"24",
"25",
"27"
] | 8C2 - 1 = 27 Answer is E
The answer is: E | E |
mathematics | If b is an even integer and b/18 is an odd integer, which of the following is NOT an even integer? | [
"(b^2)/54",
"(b^2)/8",
"(b^2)/9",
"(b^2)/6",
"(b^2)/2"
] | since b is an even integer and b/18 is an odd integer. thus maximum power of 2 in a is one. why ?? because if the power of 2 in the expression has been 2 or greater, then the b/18 must have been an even integer. (18=2*3^2. as 18 contain only one 2 in the expression)
now, any expression in which we have 4 at the denomin... | B |
mathematics | What number is obtained by adding the units digits of 734^100 and 347^83? | [
"7",
"8",
"9",
"10",
"11"
] | The units digit of 734^100 is 6 because 4 raised to the power of an even integer ends in 6.
The units digit of 347^83 is 3 because powers of 7 end in 7, 9, 3, or 1 cyclically. Since 83 is in the form 4n+3, the units digit is 3.
Then 6+3 = 9.
The answer is C.
The answer is: C | C |
mathematics | A student chose a number, multiplied it by 2, then subtracted 148 from the result and got 110. What was the number he chose? | [
"90",
"129",
"120",
"160",
"200"
] | Solution:
Let x be the number he chose, then
2*x*148=110
2x=258
x=129
correct answer B
The answer is: B | B |
mathematics | If (64)2 - (36)2 = 20 x a, then a = ? | [
"70",
"120",
"180",
"140",
"130"
] | 20 x a = (64 + 36)(64 - 36) = 100 x 28
a = (100 x 28)/20 = 140
ANSWER:D
The answer is: D | D |
mathematics | LCM of 2/7,3/14 and 5/3is | [
"45",
"35",
"30",
"25",
"None"
] | Explanation:
LCM of numerators /HCF of denominators= LCM of 2, 3, 5/HCFof7,14,3 = 30/1=30
Correct Option: C
The answer is: C | C |
mathematics | In a series of football matches, the probability that Team P wins a match against Team Q is 1/5 and the probability that the match ends in a draw is 2/3. If the two teams play five matches, what is the probability that all five matches end in a draw? | [
"2/3",
"4/9",
"8/27",
"16/81",
"32/243"
] | P(5 draws)=(2/3)^5=32/243
The answer is E.
The answer is: E | E |
mathematics | 9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen? | [
"23",
"30",
"42",
"60",
"126"
] | Out of 6 gaurds we have to select 3 -> selection means we use C -> so 6C3
Out of 3 forwards we have to select 2 -> selection means we use C -> so 3C2
Total ways = 6C3 x 3C2 = 60
ANSWER:D
The answer is: D | D |
mathematics | a train length 100 m going with speed 10m/sec another train 150m long going with speed 15m/sec.the distance between two train is 50m.then how much time second train will take to cross the first train? | [
"60sec",
"40sec",
"30sec",
"45sec",
"1min10sec"
] | net speed=15-10=5m/sec
net distance=100+150+50=300
total time =300/5=60sec
answer A
The answer is: A | A |
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. How far is the place? | [
"2.89",
"2.88",
"2.86",
"2.82",
"2.81"
] | M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88.Answer: B
The answer is: B | B |
mathematics | Ram borrowed some money at the rate of 6% p.a. for the first three years, 8% p.a.for the next six years and 10% p.a.for the period beyond nine years If the total interest paid by him at the end of 12 years is 19200, how much money did he borrow? | [
"18,000",
"10,000",
"25,000",
"20,000",
"None of these"
] | Let the sum be x. Then,
(xΓ3Γ6/100)+(xΓ6Γ8/100)+(xΓ3Γ10/100)=19200
β 18x + 48x + 30x = (19200 Γ 100)
β 96x = 1920000
β x = 20000.
Answer D
The answer is: D | D |
mathematics | A group of two women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers? | [
"7! β 2!3!2!",
"7! β 4!3!",
"5! β 3!3!",
"7 Γ 2!3!2!",
"2!3!2!"
] | 5 people can sit in 5! different ways. But because 3 men cannot sit together, we take them as a unit.
This unit of men, among themselves can sit in 3! ways.
Hence, 5! - 3!.
This unit of men along with 2 women can sit in 3! different ways which also needs to be eliminated.
Hence 5! - 3!3!
C
The answer is: C | C |
mathematics | Two taps can separately fill a cistern 5 minutes and 7.5 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in? | [
"3.8",
"3.7",
"3.6",
"3.9",
"3.5"
] | 1/5 + 1/7.5 - 1/x = 1/18
x = 3.6
Answer:C
The answer is: C | C |
mathematics | In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 1/5 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight | [
"1/7",
"1/8",
"2/5",
"3/4",
"7/8"
] | Good question.
So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).
We're told that 1/5 of the garden is green, so, since all the flowers must be either green or yellow, we know that 4/5 are yellow. We're also told there is an equal probability of straig... | C |
mathematics | M and N started a business by investing Rs.4000/- and Rs.5000/- respectively. Find the Mβs share out of a total profit of Rs.1800: | [
"Rs.500/-",
"Rs.550/-",
"Rs.600/-",
"Rs.650/-",
"Rs.800/-"
] | M = Rs.4000/-
N = Rs.5000/-
M share 4 parts & N share 5 parts
Total 9 parts -----> Rs.1800/-
----> 1 part -------> Rs.200/-
M share = 4 parts -----> Rs.800/-
E
The answer is: E | E |
mathematics | Two trains are running in opposite directions with the same speed. If the length of each train is 180 m and they cross each other in 12 sec, then the speed of each train is? | [
"54",
"77",
"36",
"88",
"21"
] | Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (180 + 180)/12 => x = 15
Speed of each train = 10 m/sec.
= 15 * 18/5 =- 54 km/hr.
Answer: A
The answer is: A | A |
mathematics | In how many ways can 5 men & 4 women can be made from a gang of 7 men & 8 women ? | [
"91",
"98",
"97",
"86",
"90"
] | Explanation:
7C5 * 8C4 = 91
A
The answer is: A | A |
mathematics | If daily wages of a man is double to that of a woman, how many men should work for 20 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600. | [
"12",
"14",
"16",
"18",
"20"
] | Explanation :
Wages of 1 woman for 1 day = 21600/40Γβ30
Wages of 1 man for 1 day = 21600Γβ2/40Γβ30
Wages of 1 man for 20 days = 21600Γβ2Γβ20/40Γβ30
Number of men = 14400/(21600Γβ2Γβ20/40Γβ30)=144/(216Γβ40/40Γβ30)= 20
Answer : Option E
The answer is: E | E |
mathematics | Find the simple interest on Rs. 70,000 at 16 2/3% per year for 9 months. | [
"7500",
"6500",
"8750",
"9500",
"None of them"
] | P = Rs.70000,R = 50/3% p.a and T = 9/12 years = 3/4years.
Simple Interest = (P*R*T)/100 = Rs.(70,000*(50/3)*(3/4)*(1/100))= Rs.8750
Answer is C.
The answer is: C | C |
mathematics | If a function f is defined by f(x)= 1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 3/2 then b= ? | [
"-3",
"1/3",
"-1/3",
"3",
"-12"
] | Given that f(x) = 1/x and f(a) = -1/2, then f(a) =1/a=-1/2 ===> a=-2, then backsolve using the answer choices:
f(ab) = f(-2b) = 1/6
A) -3 ===> f(-2*-3) = f(6) = 1/6
B) 1/3 ===> f((-2*1/3) = f(-2/3) = 1/(-2/3) = -3/2
C) -1/3 ===> f(-2*-1/3) = f(2/3) = 1/(2/3) = 3/2 WINS
D) 3 ===> f(-2*3) = f(-6) = -1/6
E) -12 ===> f(-2*... | C |
mathematics | Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 4/7 and that of Ravi is 1/5. Find the probability that both of them are selected. | [
"4/35",
"2/3",
"7/35",
"5/7",
"7/5"
] | Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 4/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 4/7 x 1/5 = 4/35
ANSWER:A
The answer is: A | A |
mathematics | How many 3 digit numbers can be formed from the digits 2,3,5,6,7 and 9 which are divisible by 5 and none of the digits is repeated? | [
"16",
"12",
"20",
"25",
"30"
] | Since each desired number is divisible by 5,
so we much have 5 at the unit place.
The hundreds place
can now be filled by any of the remaining 4 digits .
so, there4 ways of filling it.
Required number of numbers = (1 * 5 * 4)
= 20
Ans: C
The answer is: C | C |
mathematics | 56 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is : | [
"33.0",
"37.66",
"32.1",
"31.23",
"19"
] | Explanation:
Let the two parts be (56 - x) and x.
Then, 10 (56 - x) + 22x = 780
=> 12x = 220
=> x = 20.
Bigger part = (56 - x) = 37.66.
Answer: B) 37.66
The answer is: B | B |
mathematics | A firm has 4 senior partners and 6 junior partners. How many different groups F 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"
] | What seems to work as well, though its tougher to come up with this solution:
(10*9*8) * 2/3 + (10*9*4)*1/3 = 600. Divided by all possible permutations (=3!) yields 100.
Explanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has bee... | B |
mathematics | The value of (1/log3 60 + 1/log4 60 + 1/log5 60) is: | [
"0",
"1",
"5",
"60",
"2"
] | log60 3 + log60 4 + log60 5 + log60 (3*4*5)
= log60 60 = 1
ANSWER:B
The answer is: B | B |
mathematics | Due to 10% decrease in the price of sugar and John can buy 4kg more sugar in Rs100 , then find the CP of sugar? | [
"s. 1(2/9)",
"s. 2(7/9)",
"s. 2(1/9)",
"s. 3(2/7)",
"s. 4(2/9)"
] | Here r = 10 % ,x = 100 and A = 4 kg
Actual price of sugar = 10*100/((100-10 )*4) = Rs. 2(7/9)
B
The answer is: B | B |
mathematics | If y is a positive integer, which of the following could NOT be the square of y? | [
"5,228,644",
"5,224,169",
"4,989,696",
"4,985,225",
"4,998,752"
] | A number ending with 2 can never be a perfect square.
Units digit of a perfect square must be:
1,4,9,6,5
Answer E)
The answer is: E | E |
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