subject
stringclasses 1
value | question
stringlengths 3
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|---|---|---|---|---|
mathematics
|
Marks of a student were wrongly entered in computer as 83, actual marks of that student were 63. Due to this mistake average marks of whole class got increased by half (1/2). Find the total number of students in that class.
|
[
"25",
"30",
"35",
"40",
"45"
] |
Explanation:
Suppose total number of students are = X
Totalincrease=x∗1/2=x/2
=>x/2=83−63=20
=>x=40
Answer: Option D
The answer is: D
|
D
|
mathematics
|
Find the middle one when The sum of three consecutive even numbers is 36?
|
[
"10",
"12",
"14",
"16",
"18"
] |
3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
The answer is: B
|
B
|
mathematics
|
If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is Odd B)B is Odd C)AB is even
|
[
"None of the above",
"I only",
"II only",
"III only",
"III,II only"
] |
If AB is Odd then C will not even. O+E = O
If AB is even then C will not be odd.
If B is even AB is even always. But If C is Odd E+O = O
If B is Odd AB is even or odd depends on A
None of the above are true.
Answer : A
The answer is: A
|
A
|
mathematics
|
6 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
|
[
"120",
"623",
"160",
"240",
"256"
] |
it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 5
hence ans = 5 factorial = 120
hence A
The answer is: A
|
A
|
mathematics
|
What is the product of all the possible values of x if x^2+4x+7=|x+2|+3
|
[
"-6",
"–12",
"12",
"29",
"168"
] |
x^2+4x+4=|x+2|
(X+2)^2 = |x+2|
Only 3 values possible,
x = -3, x = -2, x =-1
So multiplication = -6
answer option -6
ANSWER:A
The answer is: A
|
A
|
mathematics
|
Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length D of time will elapse before they chime together again?
|
[
"2 hr. and 24 min.",
"4 hr. and 48 min.",
"1 hr. and 36 min.",
"5 hr.",
"2 hr."
] |
It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.
So the LCM of the three time intervals (18, 24,32) would be the answer.
LCM (18, 24, 32) D= 288 => 4 hours 48 mins.B
The answer is: B
|
B
|
mathematics
|
Each week, Harry is paid x dollars per hour for the first 30 hours and 2x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
|
[
"35",
"36",
"37",
"38",
"39"
] |
James worked for 41 hours hence he earned 40*x+1*2x=42x dollars;
We know that Harry also earned the same 42x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 12x additional dollars. Since for each additional hour he gets 2x dollars then he worked for 12x/2x=6 additional hours, so Harry worked for total of 30+6=36 hours.
Answer: B.
The answer is: B
|
B
|
mathematics
|
When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number?
|
[
"228",
"103",
"286",
"122",
"102"
] |
Explanation:
Let the number be x
x2 - 732 = 5280
x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609
= 10000 + 2(100)(3) + 32 = (100 + 3)2
x = 100 + 3 = 103.
Answer: B
The answer is: B
|
B
|
mathematics
|
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
|
[
"5/7",
"9/6",
"5/9",
"5/6",
"3/6"
] |
Explanation:
P(at least one graduate) = 1 - P(no graduates) =
1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6
Answer: Option D
The answer is: D
|
D
|
mathematics
|
John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/4 the number of cans that Karen collected and 1/9 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected?
|
[
"1/5",
"1/3",
"2/5",
"1/2",
"1/9"
] |
John = (1/4)Karen --> Karen = 4(John)
John = 1/9(Luke) --> Luke = 9(John)
Total = 36(John)
Karen/Total = 4/36 = 1/9
Answer: E
The answer is: E
|
E
|
mathematics
|
Two trains of equal lengths take 12 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
|
[
"16 sec",
"12 sec",
"17 sec",
"15 sec",
"23 sec"
] |
Speed of the first train = 120/12 = 10 m/sec.
Speed of the second train = 120/20 = 6 m/sec.
Relative speed = 10 + 6 = 16 m/sec.
Required time = (120 + 120)/16 = 15 sec.
Answer: D
The answer is: D
|
D
|
mathematics
|
When 7 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?
|
[
"1",
"3",
"8",
"32",
"30"
] |
Total outcome is 2^7 = 128
Favourable cases = H_ _ _ _ _ H
The second, to sixth places can be occupied by either H or T
There are 2^5 =32 ways that can be done.
Hence, the correct option is D
The answer is: D
|
D
|
mathematics
|
Of the 75 employees of a certain company, twice as many are in the sales department as are in all of the other departments combined. What is the number of employees in the sales department?
|
[
"15",
"20",
"30",
"40",
"50"
] |
This is ratio problem solving question.
I will prefer to use RMV box.
R M V
Sales 2 25 50
Other 1 25 25
Total 3 25 75
Answer is 50. i.e E
The answer is: E
|
E
|
mathematics
|
In how many ways the letters of the word LOOC be arranged?
|
[
"8",
"9",
"12",
"14",
"17"
] |
In this four letters means 4! = 24 ways
But 'O' is repeated two times.
And thus we divide the final ways by 2. I.e. there are only 24/2 = 12 ways of arranging the letters of this word.
LOOK, LOKO, LKOO, KOOL, KOLO, KLOO, OOLK, OOKL, OLOK, OKOL, OLKO, OKLO = 12 Ways
C
The answer is: C
|
C
|
mathematics
|
Set #1 = {A, B}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
|
[
"1/6",
"1/3",
"7/12",
"2/3",
"5/6"
] |
So Not a vowel in Set-1 : 1/2
And not a vowel in Ser-2:5/6
Now,
1/2∗5/6=5/12
This is for not a vowel.
Then for at least one vowel will be = 1−5/12=7/12
Answer will be C.
The answer is: C
|
C
|
mathematics
|
The average age of an adult class is 40years. 15new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?
|
[
"8",
"12",
"15",
"17",
"18"
] |
Let original strength = y
Then , 40y + 15 x 32 = ( y + 15) x 36
⇒ 40y + 480 = 36y + 540
⇒ 4y = 60
∴ y = 15
C
The answer is: C
|
C
|
mathematics
|
(51+ 52 + 53 + ... + 100) = ?
|
[
"2775",
"2785",
"2975",
"3775",
"4000"
] |
This is an A.P. in which a = 51, l = 100 and n = 50.
Sum = n (a + l) = 50 x (51 + 100) = (25 x 151) = 3775.
2 2
D)
The answer is: D
|
D
|
mathematics
|
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51
kmph, find the speed of the stream?
|
[
"16 kmph",
"19 kmph",
"14 kmph",
"17 kmph",
"13 kmph"
] |
The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream
= 51/3 = 17 kmph.
Answer: D
The answer is: D
|
D
|
mathematics
|
Find 6 + 9 + 12 + . . . + 30
|
[
"162",
"165",
"167",
"169",
"171"
] |
a = 6
l = 30
d = 9 – 6 = 3
ANSWER IS A
The answer is: A
|
A
|
mathematics
|
What least number should be added to 1056, so that the sum is completely divisible by 23
|
[
"4",
"1",
"2",
"3",
"5"
] |
Explanation:
(1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
Answer: Option C
The answer is: C
|
C
|
mathematics
|
A seller sells his apple at CP but uses a weight of 800 gm instead of kg weight. What is his profit %?
|
[
"20%",
"23%",
"25%",
"30%",
"32%"
] |
If a trader professes to sell his goods at cost price, but uses false weights, then
Gain%=[Error(True Value−Error)×100]%So here profit percentage=[200(1000−200)×100]%=[200800×100]%=25%
C
The answer is: C
|
C
|
mathematics
|
A store sells brand X pens for 5 dollars each, brand Y pens for $4 each and brand Z pens for $3 each. There are a total of 36 of these three types of pens in the store, the number of brand X pens is twice sum of the number of brand Y pens and brand Z pens, and the difference of the number of brand Y pens and the number of brand Z pens is 2. What is the largest possible total amount that three types of pens will be sold for?
|
[
"$163",
"$159",
"$156",
"$148",
"$125"
] |
Max price = 5X+4Y+3Z -------(1)
Given: X+Y+Z = 36 -------(2)
Given: X = 2(Y+Z) --------(3)
Substitute (3) in (2) Y+Z = 12 -----(4)
Given: Y-Z = 2 ----(5)
Using equations (4) and (5) Y = 7 and Z = 5.
Substitute Y and Z in 3 we get X = 24
Substitute X, Y and Z in (1) we get answer = 163 i.e.
ANSWER:A
The answer is: A
|
A
|
mathematics
|
Find 125/14*6
|
[
"2.4658",
"6.398",
"1.488",
"5.687",
"9.652"
] |
Answer=125/14*6
=125/84=1.488
Option C is correct
The answer is: C
|
C
|
mathematics
|
10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?
|
[
"5",
"6",
"7",
"8",
"9"
] |
Explanation :
Work done by 10 men in 1 day = 1/7
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 10 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/140
Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)
= 5/70 + 10/140 = 1/7
=> 5 men and 10 women can complete the work in 7 days
Answer : Option C
The answer is: C
|
C
|
mathematics
|
A sum of money lent out at S.I. amounts to Rs. 710 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
|
[
"s.440",
"s. 586",
"s. 540",
"s. 740",
"s. 840"
] |
S.I for 5 years = (1020 - 710) = Rs. 310.
S.I. for 2 years = 310/5 * 2 = Rs. 124.
Principal = (710 - 124) = Rs. 586.
ANSWER:B
The answer is: B
|
B
|
mathematics
|
Two good train each 750 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
|
[
"12 sec",
"24 sec",
"48 sec",
"72 sec",
"None"
] |
Sol.
Relative Speed = (45 + 30) km / hr
= (75 x 5 / 18) m/sec
= (125/6) m/sec.
Distance covered = (750 + 750) m = 1500m.
Required time = (1500 x 6 / 125) sec = 72 sec.
Answer D
The answer is: D
|
D
|
mathematics
|
10^(655) ÷ 10^(650) = ?
|
[
"100",
"10",
"10000",
"100000",
"1000000"
] |
10^(655) ÷ 10^(651) = 10^ (655-651) = 10^5
= 100000
Answer : D
The answer is: D
|
D
|
mathematics
|
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 8 years?
|
[
"6%",
"2.5%",
"4%",
"5%",
"3.5%"
] |
150 = (750*8*R)/100
R = 2.5%
Answer: B
The answer is: B
|
B
|
mathematics
|
A jogger running at 9 km/hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
|
[
"88",
"27",
"36",
"31",
"12"
] |
Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 190 + 120 = 310 m.
Time taken = 310/10 = 31 sec.
Answer: D
The answer is: D
|
D
|
mathematics
|
The perimeter of a semi circle is 144 cm then the radius is?
|
[
"22",
"28",
"97",
"26",
"12"
] |
36/7 r = 144 => r
= 28
Answer:B
The answer is: B
|
B
|
mathematics
|
A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 8 flight to return. In how many ways, can the boy perform his journey?
|
[
"20",
"32",
"43",
"45",
"80"
] |
Ans.(B)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 8 From, fundamental principle, total number of ways of performing the journey = 4 x 8 = 32 ways
The answer is: B
|
B
|
mathematics
|
A sum of money place at compound interest doubles itself in 6 years. In how many years will it amount to eight times itself?
|
[
"6",
"12",
"18",
"24",
"30"
] |
100 ---- 200 ---- 6
400 ---- 6
800 ---- 6
------
18 years
Answer: C
The answer is: C
|
C
|
mathematics
|
The ‘moving walkway’ is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate W of movement for his trip along the moving walkway?
|
[
"2 feet per second",
"2.5 feet per second",
"3 feet per second",
"4 feet per second",
"5 feet per second"
] |
A, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average W MUST bebetween3-6 ft per second or the Earth is FLAT!!!.
So we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft per second before he stopped walking. That leaves only answer E as plausible.
The answer is: E
|
E
|
mathematics
|
4 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
|
[
"12/9 days",
"60/13 days",
"82/8 days",
"22/76 days",
"22/2 days"
] |
4M = 6W ---- 20 days
12M + 8W -----?
18W + 8 W = 26W ---?
6W ---- 20 26 -----?
6 * 20 = 26 * x => x = 60/13 days
Answer:B
The answer is: B
|
B
|
mathematics
|
What is the probability of getting equilateral triangles from the vertices of regular hexagon?
|
[
"1/10",
"2/10",
"3/10",
"4/10",
"5/10"
] |
total no. of triangles that can b made with the vetices hexagon= 6C3=20
no. of possible outcomes i.e. no. of equality triangles=2.
.'. probability= 2/20=1/10
ANSWER:A
The answer is: A
|
A
|
mathematics
|
A boy want to make a cuboid of dimension 5m, 6m, 7m from small cubes of .04 m3. Later he realized he can make same cuboid by making it hollow. Then it takes some cubes less. What is the no. of these cubes?
|
[
"2150",
"2250",
"2350",
"2850",
"3250"
] |
volume of cuboid=5*6*7=210m3
volume of inner cuboid=(5-1)*(6-1)*(7-1)=120m3
therefore,volume of hollow cuboid=210-120=90 m3
no of cubes required=90/.04=2250 cubes
ANSWER:B
The answer is: B
|
B
|
mathematics
|
mr. depak has $419,574 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
|
[
"$1",
"$2",
"$3",
"$4",
"$0"
] |
To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,
he needs to make the total divisible by 6
Simply add the individual digits of the total = 4+1+9+5+7+4 = 30
If you add 0 , the number is divisible by 0 (30+ 0)
Correct Option : E
The answer is: E
|
E
|
mathematics
|
If x^2 – 4x = 5, then one possible value of x – 2 =
|
[
"-9",
"-5",
"-3",
"-1",
"5"
] |
x^2 – 4x = 5
i.e. x^2 – 4x - 5 = 0
i.e. x^2 – 5x + x - 5 = 0
i.e. (x-5)(x+1) = 0
i.e. x = 5 or -1
i.e. x-2 = 5-2 or -1-2
i.e. x-2 = 3 or -3
Answer: Option C
The answer is: C
|
C
|
mathematics
|
GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then HUMP?
|
[
"200",
"210",
"220",
"232",
"240"
] |
GOOD=(7+15+15+4)*4=164
BAD= (2+1+4)*3=21
UGLY= (21+7+12+25)*4=260
coding follows
(sum of position of alphabets)*(no. of letters in the given word)
so,
HUMP=(8+21+13+16)*4= 232
ANSWER:D
The answer is: D
|
D
|
mathematics
|
Two dice are rolled. What is the probability the sum will be greater than 7?
|
[
"1/9.",
"1/12.",
"5/36.",
"1/6.",
"7/36."
] |
Combinations possible: (6,6) , (5,6) , (6,5) , (5,5), (5,4) , (4,5), (4,4) = 7
Total combinations possible: 6*6=36
Answer = 7/36 Option E.
The answer is: E
|
E
|
mathematics
|
If a number is chosen at random from the set of first 20 natural numbers, The probability that it is either an even number or a prime number is?
|
[
"15/20",
"8/20",
"10/20",
"17/20",
"18/20"
] |
Explanation:
n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer is D
The answer is: D
|
D
|
mathematics
|
A man took some money for borrowed, for 3 years the total will be Rs.6500 and 5 years it will be Rs.7500/-. Then how much amount he borrowed?
|
[
"s.5000/-",
"s.5500/-",
"s.5770/-",
"s.5800/-",
"s.5820/-"
] |
3 years --------> Rs.6500/-
5 years --------> Rs.7500/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.6500/- - Rs.1500/- = Rs.5000/-
P = Rs.5000/-
A
The answer is: A
|
A
|
mathematics
|
John purchased 8kg of apples at the rate of 70 per kg and 9 kg of banana at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
|
[
"950",
"1000",
"1055",
"1060",
"1080"
] |
Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of bananas= 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055.
C)
The answer is: C
|
C
|
mathematics
|
If 3y + x > 2 and x + 2y <= 3 , What can be said about the value of y?
|
[
"y = -1",
"y >-1",
"y <-1",
"y = 1",
"y = 0"
] |
3y + x > 2 -----(1)
x + 2y < = 3
=> x + 2y + y < = 3 + y
=> x + 3y < = 3 + y -----(2)
from (1)&(2)
2 < 3y + x < 3 + y
=> 2 < 3 + y
=> -1 < y
=> y > -1
ANSWER:B
The answer is: B
|
B
|
mathematics
|
If the perimeter of a rhombus is 52 cm and one of its
diagonals is 24 cm, then the area of the rhombus is
|
[
"100 sq.cm",
"110 sq.cm",
"120 sq.cm",
"130 sq.cm",
"140 sq.cm"
] |
perimeter of rhombus = 4a (with side a)
4a=52 then a=13,
lets length of one diagonal p=24cm,
lenght of other diagonal is q;
area of rhombus = pq/2
using pythogorus theorem a^2= (p/2)^2 + (q/2)^2
we will get q=10.
then area=10*24/2=120 sq.cm
ANSWER:C
The answer is: C
|
C
|
mathematics
|
How many different positive integers are factors of 196 ?
|
[
"1",
"2",
"3",
"49",
"36"
] |
15, 14×15, 14=7^2 × 2^2
So total factors = (6+1)(6+1) = 49
Answer: D
The answer is: D
|
D
|
mathematics
|
A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
|
[
"1750",
"1900",
"8600",
"10300",
"1200"
] |
Explanation:
65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
ANSWER IS B
The answer is: B
|
B
|
mathematics
|
In an examination, 300 students appeared. Out of these students; 25 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.
|
[
"63",
"37",
"54",
"99",
"01"
] |
The number of students with first division = 25 % of 300 = 25/100 × 300 = 8400/100 = 75
And, the number of students with second division = 54 % of 300
= 54/100 × 300
=16200/100
= 162
Therefore, the number of students who just passed = 300 – (75 + 162) = 63
Answer:A
The answer is: A
|
A
|
mathematics
|
Amber works 30 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?
|
[
"m/(20d)",
"20d",
"10md/6",
"20d/m",
"30d"
] |
ANSWER: E The passage states that she works 30 days a month at d dollars per day, so 30 d is her monthly pay
The answer is: E
|
E
|
mathematics
|
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 15 minutes. How long will it take to go 5 km in stationary water?
|
[
"40 minutes",
"1 hour",
"1 hour 15 min",
"1 hour 30 min",
"1 hour 40 min"
] |
speed (upstream) =2/1 = 2 kmhr
speed (downstream)=1/(15/60)= 4 kmhr
speed in still water = 1/2 (2+4) = 3 kmhr
time taken in stationary = 5/3 = 1 hrs 40 min
ANSWER:E
The answer is: E
|
E
|
mathematics
|
Sum of two numbers is 25 and their difference is 13. Find their product.
|
[
"104",
"108",
"114",
"124",
"142"
] |
Explanation:
Friends, this sort of question is quite important in competitive exams, whenever any question come which have relation between sum, product and difference, this formula do the magic:
=>(x+y)2=(x−y)2+4xy
<=>(25)2=(13)2+4xy
<=>4xy=(25)2−(13)2
<=>xy=456/4=114
Option C
The answer is: C
|
C
|
mathematics
|
In how many ways the letters of the word RAIXBON be arranged?
|
[
"4354",
"8454",
"4356",
"5040",
"6557"
] |
Total ways of arranging the letters = 7! = 5040 ways.
D)
The answer is: D
|
D
|
mathematics
|
In 2005, 30 percent of the math department’s 40 students were female, and in 2007, 40 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
|
[
"15%",
"116%",
"136%",
"155%",
"160%"
] |
Female students in 2005 = 30% of 40 = 12
Female students in 2007 = 40% of 65 = 26
Percentage increase = [(26 - 12)/12] *100 % = 116%
Correct Option: B
The answer is: B
|
B
|
mathematics
|
A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 11,200 sedans in Anytown, how many motorcycles are there?
|
[
"1260",
"2100",
"3600",
"3200",
"5200"
] |
Let the total number of trucks = 3x
total number of sedans = 7x
total number of motorcycles = 2x
total number of sedans = 11200
=> 7x = 11200
=> x = 1600
total number of motorcycles =2x = 2*1600
=3200
Answer D
The answer is: D
|
D
|
mathematics
|
How many ways the letters of the word ‘BANKER’ can be arranged?
|
[
"600",
"650",
"720",
"750",
"7880"
] |
6P6
6!
720
C
The answer is: C
|
C
|
mathematics
|
Machines P and Q are two different machines that make items in a factory. When Machine P works alone, it covers 15 items in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 15 items in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 15item?
|
[
"m",
"n",
"15n/225-mn",
"m+n",
"m-n"
] |
working rate p = 15/m ; working rate pq =( 1/p +1/q)* n =15 or mn/15 +n/q =15 0r n/q = 15-mn/15 = 225-mn/15
q = 15n/225-mn
C
The answer is: C
|
C
|
mathematics
|
An electric pump can fill a tank in 6 hours. Because of a leak in the tank, it took 12hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
|
[
"10hours",
"12hours",
"8hours",
"5hours",
"15hours"
] |
Work done by the leak in 1 hour = 1/6 - 1/12 = 1/12
The leak will empty the tank in 12hours
Answer is B
The answer is: B
|
B
|
mathematics
|
2 no.'s, when divided by 17, leave remainders 13 and 11 respectively. If the sum of those 2 no.'s is divided by 17, the remainder will be
|
[
"5",
"6",
"7",
"8",
"9"
] |
(C)
Required remainder = remainder by (13 +11)/17 = 7
The answer is: C
|
C
|
mathematics
|
What number has a 3:4 ratio to the number 400?
|
[
"130",
"100",
"200",
"300",
"120"
] |
3:4 = x: 200
4x = 3*400
x=300
ANSWER:D
The answer is: D
|
D
|
mathematics
|
In a straight highway 2 cars starts from the same point in opposite directions each travels for 8 Kms and take left turn then travel for 6 Kms what is the distance between them now.
|
[
"16",
"20",
"25",
"10",
"15"
] |
use pythagoras theorem
c^2=a^2+b^2
=8^2+6^2 =64+36
c^2=100
c=10
the distance between A and B is (10+10)=20
ANSWER:B
The answer is: B
|
B
|
mathematics
|
Calculate the circumference of a circular field whose radius is 4 centimeters.
|
[
"2",
"4",
"6",
"8",
"10"
] |
Circumference C is given by
C = 2πr = 2π*4 = 8 π cm
correct answer D
The answer is: D
|
D
|
mathematics
|
The cash difference between the selling prices of an article at a profit of 2% and 6% is Rs 3. The ratio of two selling prices is
|
[
"51:53",
"52:53",
"53:54",
"54:55",
"None of these"
] |
Explanation:
Let the Cost price of article is Rs. x
Required ratio = (102% of x) / (106% of x)
=102/106
=51/53 = 51:53.
Answer: A
The answer is: A
|
A
|
mathematics
|
At 15:15 pm railway time, what will be the angle between minute and hour hand?
|
[
"238",
"360",
"377",
"277",
"291"
] |
At 15:15 both minute and hour hands will be in same position. Hence the angle between them will be zero
degrees. However 360 degree also means both minute and hour hands are in same position. Hence correct answers are
both zero and 360 degrees
Answer:B
The answer is: B
|
B
|
mathematics
|
If the wheel is 42 cm then the number of revolutions to cover a distance of 1056 cm is?
|
[
"18",
"4",
"6",
"8",
"19"
] |
2 * 22/7 * 42 * x = 1056
=> x = 4
Answer: B
The answer is: B
|
B
|
mathematics
|
an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -y and a*y=0, then y=?
|
[
"a) -a",
"b) -1/a",
"c) 1/a",
"d)0",
"e)a"
] |
If a*y=0 and a=-y then a-y = o of a=y, so answer E
The answer is: E
|
E
|
mathematics
|
What is the least number of square tiles required to pave the floor of a room
15 m 17 cm long and 9m 2 cm broad?
|
[
"814",
"802",
"836",
"900",
"1000"
] |
L = 15 M 17 CM =1517 CM
B = 9 M 2 CM = 902 CM^2
AREA = 1517 * 902 CM^2
FIND OUT HCF = 41
AREA OF SQUARE = 41 * 41 = 1517 * 902 / 41 * 41 = 37 * 22
=407 * 2 =814
ANSWER A
The answer is: A
|
A
|
mathematics
|
A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,000 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
|
[
"25",
"30",
"35",
"39",
"45"
] |
Day 1
2t+3=21
t=9
Day 2
t+3
9+3=12
9r+12(r+15)=1000
r=39
Answer:D
The answer is: D
|
D
|
mathematics
|
A line that passes through (–1, –4) and (3, k) has a slope = k. What is the value of k?
|
[
"3/4",
"1",
"4/3",
"2",
"7/2"
] |
This is a considerably more difficult one, which will involve some algebra. Let’s say that the “first” point is (–1, –4) and the “second,” (3, k). The rise = k + 4, which involves a variable. The run = 3 – (–1) = 4. There the slope is (k + 4)/4, and we can set this equal to k and solve for k.
{{k + 4}/4} = k
k + 4 = 4k
4 = 3k
k = 4/3
Answer = C
The answer is: C
|
C
|
mathematics
|
Which of the following number should be added to 11158 to make it exactly divisible by 77?
|
[
"6",
"5",
"8",
"7",
"9"
] |
Ondividing 11158 by 77, the remainder is 70
Thus, Number to be added = (77 - 70)=7
ANSWER:D
The answer is: D
|
D
|
mathematics
|
At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $10 on candy, how much did John spend at the supermarket?
|
[
"$60",
"$80",
"$90",
"$120",
"$150"
] |
Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.
We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $10 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:
(1/2)T + (1/3)T + (1/10)T + 10 = T
To get rid of the fractions we can multiply the entire equation by 30, and we obtain:
15T + 10T + 3T + 300 = 30T
28T + 300 = 30T
300 = 2T
T = 150
John spent $90 at the supermarket.
Answer: E
The answer is: E
|
E
|
mathematics
|
The length of a rectangle is reduced by 30%. By what % would the width have to be increased to maintain the original area?
|
[
"42.8%",
"20%",
"25%",
"30%",
"35%"
] |
Sol. Required change = (30*100)/(100-30)=42.8%
A
The answer is: A
|
A
|
mathematics
|
The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).
|
[
"178.27",
"178.29",
"178.21",
"178.19",
"178.55"
] |
Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm
= 180 * 35 cm - 166 cm + 106 cm/35 = 180 cm - 60 /35 cm
= 180 cm - 1.71 cm = 178.29 cm.Answer:B
The answer is: B
|
B
|
mathematics
|
George baked a total of 75 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
|
[
"5",
"4",
"2",
"6",
"7"
] |
3/5 of the 75 pizzas cooked on Saturday = 45 pizzas
3/5 of the remaining pizzas on Sunday = 18 pizzas
We're left with (75-45-18) =12 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.
M T W TH F
5 4 2 1 0 =12
W=2
C
The answer is: C
|
C
|
mathematics
|
Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 15 kmph and 25 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?
|
[
"144",
"36",
"124",
"32",
"38"
] |
Time taken to meet the first time = length of track/relative speed
= 400/ (15 +25) (5/18)
= 400/40 *(18/5) = 36 sec.
Answer : B
The answer is: B
|
B
|
mathematics
|
A circular mat with diameter 18 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
|
[
"5/12",
"3/5",
"1/2",
"3/8",
"5/6"
] |
SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (3)(9)(9)
Area of the Table = (24)(24)
So the quick way to estimate is looking at the fraction like this: (3/24)(81/24)
I hope this is easy to follow, so with some simplification i get (1/8)(3) = (3/8) Answer is D
The answer is: D
|
D
|
mathematics
|
7, 26, 63, 124, 215, 342, (....)
|
[
"481",
"511",
"421",
"391",
"515"
] |
The series is (23 - 1), (33 - 1), (43 - 1), (53 - 1), (63 - 1), (73 - 1), ...
Hence, next number is (83 - 1) = 511
Answer is B
The answer is: B
|
B
|
mathematics
|
It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number B?
|
[
"a. 2^96 + 1",
"b. 2^16 - 1",
"c. 2^16 + 1",
"d. 7 * 2^33",
"e. 2^64 + 1"
] |
a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of B= (a+b) is a factor of (a³ + b³)
Henca A
The answer is: A
|
A
|
mathematics
|
When positive integer n is divided by 7, the remainder is 1. When n is divided by 11, the remainder is 5. What is the smallest positive integer k such that k+n is a multiple of 77?
|
[
"2",
"4",
"6",
"8",
"10"
] |
n = 7p + 1 = 11q + 5
n+6 = 7p + 7 = 11q + 11
n+6 is a multiple of 7 and 11, so it is a multiple of 77.
The answer is C.
The answer is: C
|
C
|
mathematics
|
Find the H.C.F. and L.C.M. of 2/3, 8/9, 16/81 and 10/27.
|
[
"2/81 and 80/3",
"1/80 and 70/2",
"1/90 and 60/3",
"1/75 and 40/5",
"None of them"
] |
H.C.F. of given fractions = H.C.F. of 2,8,16,10/L.C.M. of 3,9,81,27 = 2/81
L.C.M of given fractions = L.C.M. of 2,8,16,10/H.C.F. of 3,9,81,27 = 80/3
Answer is A.
The answer is: A
|
A
|
mathematics
|
Farmer Charlie has a chicken farm. On a certain day, Charlie calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.
One chicken lays two eggs in three days. How many eggs do three chickens lay in nine days?
|
[
"11",
"17",
"18",
"20",
"23"
] |
C
18
1 chicken lays 2 eggs in 3 days, so 3 chickens lay 3×2=6 eggs in 3 days. In 9 days, these 3 chickens lay 3 times as much eggs as in 3 days. Conclusion: three chickens lay 3×6=18 eggs in nine days.
The answer is: C
|
C
|
mathematics
|
Amy has to go to three different stores this week. How many ways can she go to one or more stores today?
|
[
"19",
"26",
"24",
"9",
"7"
] |
Amy has to visit at least one of three stores.
= > 2^3 - 1 = 7
E
The answer is: E
|
E
|
mathematics
|
he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg. What might be the weight of the new person ?
|
[
"90 kg",
"55 kg",
"45 kg",
"85 kg",
"25 kg"
] |
Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (70 + 20) kg = 90 kg.
Answer: A
The answer is: A
|
A
|
mathematics
|
Two pipes A and B can fill a tank in 10 minutes and 20 minutes respectively. If both the taps are opened simultaneously, and the tap A is closed after 5 minutes, then how much more time will it take to fill the tank by tap B?
|
[
"5min",
"6min",
"10min",
"7min",
"12min"
] |
Part filled in 5 min. = 5(1/10 + 1/20) = 5*3/20 = 3/4
Remaining part = 1 - 3/4 = 1/4
Part filled by B in 1min. = 1/20
1/20 : 1/4 :: 1:x
x = 1/4 *1 * 20 = 5min
Answer is A
The answer is: A
|
A
|
mathematics
|
A 5 litre jug contains 4 litres of a salt water solution that is 15 percent salt. If 1.5 litres of the solution spills out of the jug, and the jug is then filled to capacity with water,approximately what percent of the resulting solution in the jug is salt?
|
[
"7.5%",
"8.5%",
"9.5%",
"10.5%",
"11.5%"
] |
A 5 litre jug contains 4 litres of a salt water solution that is 15 percent salt. If 1.5 litres of the solution spills out of the jug,then 2.5 ltrs of solution with 15% salt is left in jug.
If solution is now increased to 5 ltrs, the volume is doubled, then salt percentage is halved to 7.5%.
ANSWER:A
The answer is: A
|
A
|
mathematics
|
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 363 sq m, then what is the breadth of the rectangular plot?
|
[
"11",
"17",
"18",
"101",
"1322"
] |
Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 363
3b2 = 363
b2 = 121 = 11 (b > 0)
b = 11 m.
Answer: A
The answer is: A
|
A
|
mathematics
|
A circular path of 19 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
|
[
"rs.49.25",
"rs.40.50",
"rs.44.20",
"rs.62.85",
"rs.43.10"
] |
Explanation:
π (21^2 - 19^2) = 22/7 * (441-361) = 251.43
251.43 * 1/4 = Rs.62.85
Answer: Option D
The answer is: D
|
D
|
mathematics
|
Hari spends 50% of his income. His income is increased by 10% and he increased his expenditure by 5%. Find the percentage increase in his savings?
|
[
"10%",
"15%",
"20%",
"25%",
"30%"
] |
Let original income = $100
expenditure = $50
savings = $50
new income = $110
new expenditure = $105/100 * 50 = $105/2
New savings = 110 - 105/2 = $115/2
Increase in savings = 115/2 - 50 = $15/2
Increase % = 15/2 * 1/50 * 100 = 15%
Answer is B
The answer is: B
|
B
|
mathematics
|
What is the greatest value of positive integer x such that 2^x is a factor of 100^60?
|
[
"100",
"110",
"120",
"105",
"115"
] |
Put in simple words, we need to find the highest power of 2 in 100^60
100 = 2^2*5^2
Therefore 100^60 = (2^2*5^2)^60 = 2^120*5^120
Answer : C
The answer is: C
|
C
|
mathematics
|
|16 - 5| - |5 - 12| = ?
|
[
"3",
"2",
"1",
"0",
"4"
] |
|16 - 5| - |5 - 12| = | 11 | - | -7 | =11 - 7 = 4
correct answer E
The answer is: E
|
E
|
mathematics
|
The average (arithmetic mean) of the even integers from 0 to 100 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 50 inclusive?
|
[
"24",
"25",
"26",
"48",
"50"
] |
So, according to A mean of a set of even numbers from 0 to 100 =(0+100)/2=50 and mean of a set of even numbers from 0 to 50 =(0+50)/2=25
Difference=50-25=25
Answer: B.
The answer is: B
|
B
|
mathematics
|
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream?
|
[
"10 kmph",
"17 kmph",
"19 kmph",
"17 kmph",
"20 kmph"
] |
Speed of the boat in still water
= (60+100)/2
= 80 kmph. Speed of the stream
= (100-60)/2
=20 kmph.
Answer: E
The answer is: E
|
E
|
mathematics
|
A certain manufacturer increased its gross profit on a product from 10 percent of the cost of the product to 15 percent of the cost by changing the selling price. If the new selling price was $92.00 and the cost of the product remained the same, what was the old selling price?
|
[
"$77.40",
"$80.00",
"$83.64",
"$87.40",
"$88.00"
] |
Given that {cost of the product}*1.15=$92 --> {cost of the product}=$80.
The old price was $80*1.1=$88.
Answer: E.
The answer is: E
|
E
|
mathematics
|
Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 48 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
|
[
"72 sec",
"132 sec",
"157.5 sec",
"252 sec",
"None"
] |
Solution
Relative Speed = (48 - 40 ) Kmph
= 8 kmph
=(8 x 5 / 18)m/sec
= (40 / 18 ) m/sec
Time taken = (350 x 18 / 40) sec
= 157.5 sec.
Answer C
The answer is: C
|
C
|
mathematics
|
What is the remainder when 43^87 is divided by 5?
|
[
"0",
"1",
"2",
"3",
"4"
] |
The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}
87 has the form 4k+3 so the units digit of 43^87 is 7.
The remainder when dividing by 5 is 2.
The answer is C.
The answer is: C
|
C
|
mathematics
|
What will be the result of 12^4+ 3 +2^9 +3 - 8/2 ?
|
[
"58",
"14",
"145",
"69",
"74"
] |
The multiplication(e.g. 12^4) and division(e.g. 8/2) is done first and then the sum(e.g. 48+3) and
subtraction (e.g.4-4), and the answer is 69, option D.
The answer is: D
|
D
|
mathematics
|
Tina and Rebecca had the same number of candies. Tina gave Rebecca 20 candies so that now Rebecca has five times as many candies as Tina has. Rebecca has now how many candies?
|
[
"50",
"48",
"54",
"55",
"60"
] |
T = R
T - 20 ;R + 20
R + 20 = 5 ( T - 20 )
R + 20 =5T - 100
R - 5T = - 120
We knowR = T, so
R - 5T = - 120
Or, R - 5R = -120
Or, - 4R = - 120
Or, R = 30( This is the initital no of Candies Rebecca had)
Candles now she possesses is30+ 20 = 50
So , Rebecca now has 50 candies.
Answer will be (A) 50
The answer is: A
|
A
|
mathematics
|
A train travels 240 km in 3 hours and 450 km in 5 hours.find the average speed of train.
|
[
"80 kmph",
"60 kmph",
"86 kmph",
"90 kmph",
"None of these"
] |
As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 240 + 450 = 690 km
Thus, Total Speed = 8 hrs
or,Average Speed = 690/8
or, 86kmph.
ANSWER:C
The answer is: C
|
C
|
mathematics
|
A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
|
[
"6 days",
"9 days",
"18 days",
"24 days",
"4 days"
] |
Explanation:
3/12 + (3 + x)/16 = 1
x = 9 days
Answer B
The answer is: B
|
B
|
mathematics
|
How long does a train 110 m long running at the speed of 36 km/hr takes to cross a bridge 132 m length?
|
[
"82.1 sec",
"12.1 sec",
"24.2 sec",
"13.1 sec",
"12.15sec"
] |
Speed = 36 * 5/18 = 10 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/10 = 24.2 sec.
Answer:C
The answer is: C
|
C
|
mathematics
|
At what rate percent on simple interest will a sum of money double itself in 50 years?
|
[
"3 1/3%",
"3 1/9%",
"3 9/3%",
"2%",
"3 6/3%"
] |
P = (P*50*R)/100
R = 2%
Answer: D
The answer is: D
|
D
|
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