subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | A, B and C can independently complete a piece of work in 8,12 and 6 days respectively. A and B work together for 4 days and leave. How long will C take to finish the remaining work? | [
"1",
"2",
"3",
"4",
"5"
] | A and B work together for 4 days and completed 4*(1/8 +1/12) =5/6 work.
Balance 1/6 work will be completed by C in one day.
ANSWER:A
The answer is: A | A |
mathematics | If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y − 2)
II. z<(x − 1)/(y − 2)
III. z>(x + 1)/(y + 2) | [
"I only",
"I and II",
"II and III",
"II only",
"I and III"
] | x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z>(x − 1)/(y − 2) --> 2/3 > 1/1 --> False
II. z<(x − 1)/(y − 2) --> 2/3 < 1/1 --> True
III. z>(x + 1)/(y + 2) --> 2/3 > 3/5 --> True
Answer: C
The answer is: C | C |
mathematics | What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ? | [
"9800",
"9600",
"9400",
"9500",
"9200"
] | Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600
answer :B
The answer is: B | B |
mathematics | Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 72 floors per minute. At the same time Joyce gets on an elevator on the 61st floor of the same building and rides down at a rate of 78 floors per minute. If they continue traveling at these rates, at which floor will their paths cross? | [
"19",
"28",
"30",
"35",
"44"
] | Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 72 floors per minute. At the same time Joyce gets on an elevator on the 61st floor of the same building and rides down at a rate of 78 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?... | D |
mathematics | The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 432 sq m, then what is the breadth of the rectangular plot? | [
"12",
"17",
"18",
"19",
"14"
] | Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 432
3b2 = 432
b2 = 144
b = 12 m.
Answer: Option A
The answer is: A | A |
mathematics | There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total W of the book? | [
"3003",
"3027",
"3024",
"3021",
"3018"
] | First, you have to find the common ratio for all 3 books. You have:
P:C:B
3:2 --> multiply by 2 (gives you row 3)
4:6
6:4:3
Hence:
P:C:B:T(Total)W
6:4:3:13 ----> This means, the Total Number must be a multiple of 13.
Answer A is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
The answer is... | A |
mathematics | Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is? | [
"1 : 3",
"3 : 2",
"3 : 4",
"4 : 3",
"3 : 5"
] | Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
( 27x + 17y ) / (x+ y )= 23
=> 27x + 17y = 23x + 23y
=> 4x = 6y
=> ( x/y ) = ( 3/2 )
Answer: Option B
The answer is: B | B |
mathematics | In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes. | [
"10",
"12",
"13",
"15",
"16"
] | Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
The answer is: B | B |
mathematics | Find the wrong number below mentioned series
11,150,280,560,800 | [
"800",
"560",
"280",
"150",
"11"
] | 11 is the only prime number or odd number in the series.
ANSWER:E
The answer is: E | E |
mathematics | A man can row at 5 kmph in still water .If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back ,how far is the place ? | [
"2.4 km",
"2.5 km",
"3 km",
"3.6 km",
"None of these"
] | Answer A
Solution
Speed downstream = kmph = 6 kmph,Speed upstream = (5 - 1)
kmph = 4 kmph.
Let the required distance be x km.
Then,x/6 + x/4 = 1 => 2x + 3x = 12 5x = 12=> x = 2.4 km. Answer A
The answer is: A | A |
mathematics | If .005^4 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain? | [
"0",
"8",
"9",
"10",
"11"
] | 0.005^4= (5*10^-3)^4 = 625*10^-12 = 0.625*10^-9 which would have 9 zeros to the right of the decimal point. The answer is C.
The answer is: C | C |
mathematics | In a river flowing at 2 km/hr, a boat travels 40 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time. | [
"10 hours",
"12 hours",
"14 hours",
"15 hours",
"None of these"
] | Explanation :
speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 40 km
Total time taken = Time taken downstream + Time taken upstream
= (40/8) + (40/4) = 15
D
The answer is: D | D |
mathematics | My 5 sons are enrolled in an army's platoon of 80 men. The General is choosing randomly 2 men to a suicide mission. What is the probability of both of the selected men will be two of my sons? | [
"1/80",
"2/80",
"5/80",
"1/316",
"2/316"
] | My sons are 5 in a group of 80 men. Thus the probability of choosing 2 of my sons is: (5/80)(4/79) = 1/316. The correct answer is D.
The answer is: D | D |
mathematics | P, Q and R have $4000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R? | [
"2400",
"2403",
"3998",
"2539",
"1600"
] | E
1600
Let the amount with R be $ r
r = 2/3 (total amount with P and Q)
r = 2/3(4000 - r) => 3r = 8000 - 2r
=> 5r = 8000 => r = 1600.
The answer is: E | E |
mathematics | Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.5400. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu? | [
"s.750, Rs.2250",
"s.2000, Rs.750",
"s.750, Rs.2000",
"s.800, Rs.1250",
"s.900, Rs.2700"
] | Minu’s one day’s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18
Anu’s wages: Binu’s wages: Minu’s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2
Minu’s share = Rs.5400* 2/12 = Rs.900
Anu’s share = Rs.5400* 6 /12 = Rs.2700
ANSWER:E
The answer is: E | E |
mathematics | 375 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees | [
"10",
"12",
"14",
"16",
"15"
] | 26 trees have 25 gaps between them,
Required distance (375/25) = 15
E
The answer is: E | E |
mathematics | The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 4, the average of the numbers increases to 9.2. What number is multiplied by 4? | [
"1.5",
"3.0",
"3.9",
"4.0",
"6.0"
] | The average of 5 numbers is 6.8
The sum of 5 numbers will be 6.8 x 5 = 34
The average of 5 number after one of the number is multiplied by 4 is 9.2
The sum of the numbers will now be 9.2 x 5 = 46
So the sum has increased by 46-34 = 12
Let the number multiplied by 4 be n
Then,
4n = n+12
or 3n = 12
or n = 4
Answer:- D
Th... | D |
mathematics | A can do a piece of work in 20 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work? | [
"18",
"77",
"66",
"55",
"10"
] | 8/20 + 6/x = 1
X = 10 days
Answer:E
The answer is: E | E |
mathematics | Let R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n , n>= 144. Find R1+R2. | [
"90",
"82",
"84",
"64",
"None"
] | Explanation :
The remainder when 276 divided by 91 is 3 hence
remainder of (276)n/91 = remainder 3n/91
Taking n = 1,2,3,4,5
We get the possible remainders as 3, 9, 27, 81, 61, 1 respectively.
For n>5, the pattern repeats
Hence R1 = 81 and R2 = 1
R1+R2 = 81+1 = 82
Answer : B
The answer is: B | B |
mathematics | 2 men and 4 boys can complete a work in 4 days. 5 men and 6 boys can complete the same work in 3 days. The work done by 2 boys is equal to the work of how many men? | [
"4",
"5",
"6",
"7",
"8"
] | Exp: (2m + 4b)’s one day’s work = 1/4
(5m + 6b)’s one day’s work = 1/3
=> (8m + 16b)’s one day’s work = (15m + 18b) ’s one day’s work
=> 7 men’s work = 2 boy’s work
So, we should be employ 5 more men to be completed the work.
Answer: B
The answer is: B | B |
mathematics | In a box of 8 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective? | [
"1/12",
"5/14",
"2/13",
"2/15",
"1/17"
] | First, there are 6C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 8C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 6C3/8C3=20/56 = 5/14
Answer is B
The answer is: B | B |
mathematics | A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, “How many gold coins do we have?” After pausing a moment, he replied, “Well! If I divide the coins into two unequal numbers, then 37 times the difference between the two numbers equals the difference betw... | [
"36",
"37",
"38",
"39",
"40"
] | 37(x-y)=x^2-y^2. u no tht x^2-y^2=(x-y)(x+y).so (x-y) cancels on both sides to give x+y=37.so sum of unequal halves=37 which is the required answer.
Answer B
The answer is: B | B |
mathematics | Peter age after 5 years will be 5 times his age 5 years back. what is the present age of Peter? | [
"A)20",
"B)25",
"C)15",
"D)22",
"E)10"
] | Peter present age= x
after 5 years = x+5
5 years back = x-5
x+5= 5(x-5)
x=20
Answer is A
The answer is: A | A |
mathematics | When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 728 more than 4times the middle integer. Find the numbers? | [
"650",
"678",
"698",
"728",
"729"
] | x + 4 (x + 4) = 728 + 4 (x + 2)
Solve for x and find all three numbers
x + 4 x + 16 = 728 + 4 x + 8
x = 720
x + 2 = 722
x + 4 = 724
Check: the smallest is added to four times the largest
720 + 4 * 724 = 3616
four times the middle
4 * 722 = 2888
3616 is more than 2888 by
3616 - 2888 = 728
D
The answer is: D | D |
mathematics | Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? | [
"1040",
"1050",
"1055",
"1065",
"1075"
] | Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055
C
The answer is: C | C |
mathematics | A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 20 as remainder. Find the no. is? | [
"122456",
"220020",
"220022",
"235467",
"220026"
] | (555 + 445) * 2 * 110 + 20 = 220000 + 20 = 220020
B
The answer is: B | B |
mathematics | A person invested in all Rs. 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is? | [
"3477",
"2688",
"2699",
"1200",
"2671"
] | Let the parts be x, y and [2600 - (x + y)].
Then,
(x * 4 * 1)/100 = (y * 6 * 1)/100 = {[2600 - (x + y)] * 8 * 1}/100
y/x = 4/6 = 2/3 or y = 2/3 x
So, (x * 4 * 1)/100 = [(2600 - 5/3 x) * 80/100
52x = (7800 * 8) => x = 1200
Money invested at 4% = Rs. 1200.
Answer:D
The answer is: D | D |
mathematics | Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 9/10, what is the probability that Taylor makes exactly one basket in three tries? | [
"3^5/10^3",
"3^4/10^3",
"3^3/10^3",
"3^2/10^3",
"3^4/10^4"
] | Probability of basket = 1/10
Probability of no basket = 9/10
Required probability= 3* (1*9*9/1000)
= 3^5/10^3
A is the answer
The answer is: A | A |
mathematics | A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year? | [
"3:5",
"3:4",
"3:8",
"3:9",
"3:1"
] | They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B
=6000 : 8000 => 3:4
Answer:B
The answer is: B | B |
mathematics | What is the sum of all three digit integers formed using the digits 1, 2, and 3 (repetition is allowed) | [
"4443",
"5980",
"5992",
"5990",
"5994"
] | n = 3*3*3 = 27
<x> = (333 + 111) / 2 = 222
Sum = number of integers x average value
n * <x> = 27 * 222 = 5994
answer = E
The answer is: E | E |
mathematics | A rectangular ground is to be filled with square tiles of unit area. The border of the ground should be of red coloured tiles and inside white. If the number of red and white tiles are the same, find the minimum dimensions of the ground. | [
"44",
"45",
"46",
"47",
"48"
] | Let us consider R for RED & W for WHITE
[R01][R02][R03][R04][R05][R06][R07][R08]
[R24][W01][W02][W03][W04][W05][W06][R09]
[R23][W07][W08][W09][W10][W11][W12][R10]
[R22][W13][W14][W15][W16][W17][W18][R11]
[R21][W19][W20][W21][W22][W23][W24][R12]
[R20][R19][R18][R17][R16][R15][R14][R13]
In this rectangle there are 24 RED... | E |
mathematics | The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is? | [
"2 years",
"6 years",
"7 years",
"9 years",
"4 years"
] | Amount = (30000 + 4347) = Rs. 34347
Let the time be n years. Then,
30000(1 + 7/100)n = 34347
= (107/100)n = 34347/30000 = (107/100)2
n = 2 years.
Answer: A:
The answer is: A | A |
mathematics | The ratio of the radius of two circles is 2: 5, and then the ratio of their areas is? | [
"4:25",
"2:9",
"1:9",
"3:7",
"3:4"
] | r1: r2 = 2: 5
Î r1^2: Î r2^2
r1^2: r2^2 = 4:25
Answer: A
The answer is: A | A |
mathematics | One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field. | [
"120m2",
"130m2",
"140m2",
"150m2",
"160m2"
] | Explanation:
We know h2=b2+h2
=>Other side
=√(17)2−(15)2
=√289−225
=√64
=√8meter
Area=Length×Breadth
=15×8m2=120m2
ANSWER IS A
The answer is: A | A |
mathematics | In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability W at least one of the shirts he draws will be blue? | [
"25/153",
"28/153",
"5/17",
"4/9",
"W=12/17"
] | P(at least one blue) = 1- P(0 blue) = 1 - 10/18*9/17 =W= 12/17.
Answer: E.
The answer is: E | E |
mathematics | A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the
mixture must be drawn off and replaced with water so that the mixture may be half water and half
syrup? | [
"13",
"14",
"15",
"16",
"17"
] | Explanation :
Let the quantity of the initial liquid in the vessel = 8 litre and quantity of water in the initial liquid = 3
litre andquantity of syrup in the initial liquid = 5 litreLet x litre of the mixture is drawn off and replaced
with waterQuantity of water in the new mixture = 3−3x8+xQuantity of syrup in the new... | C |
mathematics | Andy solves problems 74 to 135 inclusive in a Math exercise. How many problems does he solve? | [
"53",
"62",
"51",
"50",
"49"
] | 135-74+1= 62
'B' is the answer
The answer is: B | B |
mathematics | Consider a right triangle WBC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle WBC | [
"[A] x+y+z/3",
"[B] x-y+z/3",
"[C] x-y+z/2",
"[D] (x^2 + y^2 + z^2)/3",
"[E] cannot be determined"
] | Radius of a circle inscribed in the right triangle WBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.
Answer: C
The answer is: C | C |
mathematics | Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 105 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the as... | [
"15%",
"20%",
"25%",
"66 2/3%",
"40%"
] | 0.4*75 + 0.6x = 105
30 + 0.6x=107
0.6x = 75
x= 125
125/75= 1.66666...
Ans:D
The answer is: D | D |
mathematics | If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.65 then sum is | [
"s.5000",
"s.6500",
"s.5800",
"s.6000",
"s.6200"
] | p(r/100)^2=C.I-S.I
P(10/100)^2=65
6500
ANSWER:B
The answer is: B | B |
mathematics | The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 330 the Other is | [
"330",
"300",
"210",
"250",
"350"
] | The other number
= L.C.M * H.C.F/given number
= 2310*30/330 = 210
Answer is C.
The answer is: C | C |
mathematics | A sum of money at simple interest amounts to Rs.720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is : | [
"400",
"500",
"600",
"700",
"800"
] | SI of 5 year = (1020-720)=300
so, SI of 1 year=300/5=60
so, SI of 2 year=60*2=120
so, sum is =(720-120)=600
ANSWER:C
The answer is: C | C |
mathematics | Which of the following is true about 0<|x|-2x<5? | [
"-1<x<0",
"0<x<1",
"1<x<2",
"2<x<3",
"3<x<4"
] | when can be |x|-2x be greater than 0..
NEVER when x is positive..
ONLY A is left..
you can also substitute any value within the given range to check for answer
Example - put x as -0.5 for A. -1<x<0..
so |x|-2x = |-0.5|- 2*(-0.5) = 0.5+1 = 1.5 and it satisfies 0<|x|-4x<5
A
The answer is: A | A |
mathematics | If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is? | [
"1.44%",
"2.45%",
"7.44%",
"8.44%",
"2.44%"
] | Explanation:
SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
Answer: A
The answer is: A | A |
mathematics | An insect leaps 72 centimeters in 1.5 seconds. What is its speed? | [
"90 centimeters per second",
"10.8 centimeters per second",
"1.08 meters per second",
"4.8 centimeters per second",
"0.48 meters per second"
] | 72 / 1.5 = 48 cm/s = 0.48 m/s
The answer is E.
The answer is: E | E |
mathematics | There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback? | [
"75",
"120",
"210",
"246",
"252"
] | Paperbacks - 4, hardbacks - 6
5 books in total and at least 1 from each.
Total combinations for 5 books = (1pb, 4 hb) + (4pb, 1hb) + (3pb, 2hb) + (2pb, 3hb)
1pb, 4hb = 4c1*6c4 = 60
4pb,1hb = 4c4*6c1 = 6
3pb,2hb = 4c3*6c2 = 60
2pb,3hb = 4c2*6c3 = 120
Total combinations of 5 books = 60+6+60+120 = >246
Ans D.
The answer i... | D |
mathematics | A cyclist covers a distance of 750 meter in 2 minutes 40 seconds. What is the speed in km/hr of cyclist | [
"16 km/hr",
"16.85 km/hr",
"18 km/hr",
"19 km/hr",
"20 km/hr"
] | Explanation:
Speed=Distance/Time
Distance=750meter
Time=2 min 40sec=160sec
Speed=750/160=4.68m/sec
=>4.68∗18/5km/hr=16.85km/hr
Option B
The answer is: B | B |
mathematics | There are some 2 wheelers and 4 wheelers parked total number of wheels present is 240 then how many 4 wheelers were there | [
"20",
"30",
"40",
"50",
"60"
] | 2x+4x=240;
x=40;
then two whl=2*40=80
4 whl =4*40=160;
ans: 160/4= i-e 40
ANSWER:C
The answer is: C | C |
mathematics | Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 90% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above? | [
" 5%",
" 10%",
" 15%",
" 55%",
" 30%"
] | Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.
Neither is zero.
Hence 100 = 90 + 50 + 35 - n (Exactly 2 products) - 2*10
100 = 155 - n (Exactly 2 products) => n (Exactly 2 products) = 55.
Answer: D
The answer is: D | D |
mathematics | A sum of money deposited at C.I. amounts to Rs.1980 in 3 years and to Rs.2492 in 4 years. Find the rate percent? | [
"30%",
"10%",
"25%",
"19%",
"50%"
] | 1980--- 512
100 --- ? => 25%
Answer: C
The answer is: C | C |
mathematics | A veterinarian surveys 26 of his patrons.He discovers that 14 have dogs, 10 have cats, and 5 have fish.Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish.If no one has all three kinds of pets, how many patrons have none of these pets? | [
"3",
"4",
"5",
"6",
"7"
] | no. of patron have dogs = 14
no. of patron have cats = 10
no. of patron have fish = 5
no. of patron have dogs and cats = 4
no. of patron have dogs and fish = 3
no. of patron have cats and fish = 1
no. of patron have all three pets = 0
no. of patron have only dogs = 7
no. of patron have only cats = 5
no. of patron have ... | C |
mathematics | There are 192 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ? | [
"72",
"85",
"107",
"98",
"108"
] | You had the answer almost right. The x = 84 refers to ONLY set A.
However what's being asked is how many members are part of set A. This will include:
1. Only Set A
2. Set A and Set B
So the answer is Set A = 84+ Set AB = 84+23 = 17
C
The answer is: C | C |
mathematics | The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero? | [
"18",
"16",
"17",
"19",
"13"
] | Average of 20 numbers = 0
Sum of 20 numbers = (0 * 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).
Answer:D
The answer is: D | D |
mathematics | After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 75%?
M13-03. | [
"N−35",
"N+72",
"2N+78",
"2N+72",
"2N−35"
] | Say N=1.
So, after 1 test John has 70 correct answers.
In 2 tests, so in 200 questions he needs to have 0.75*200=150 correct answers, so in the second test he must get 150-70=80 questions correctly.
Now, plug N=1 into the answer choices to see which one yields 80. Only option D fits.
Answer: C.
The answer is: C | C |
mathematics | A certain smoothie A is three-fifths blueberries and 40% raspberries by weight. Another smoothie B is three-quarters banana and one-quarter raspberries by weight. If the mixed smoothie of A and B is 30% raspberries by weight, how much weight of this mixture belongs to smoothie A? | [
"10%",
"33.33%",
"45%",
"50%",
"66.66%"
] | A is 40% raspberries;
B is 25% raspberries.
A and B is 30% raspberries;
30% raspberries in the mixed smoothie of A and B come from 40% raspberries in A and 25% raspberries in B, thus:
0.3(A+B)=0.4A+0.25B --> 0.1A=0.05B --> A/B=1/2 --> A/(A+B)=1/3.
Answer: B.
The answer is: B | B |
mathematics | Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 8, how many people got on at the first stop? | [
"128",
"64",
"32",
"16",
"8"
] | 7 - > 1
6 - > 2
5 - > 4
4 - > 8
3 - > 16
2 - > 32
1 - > 64
because people get off after the first stop
=> the formula will be : 2^(n-1) where n is the stop number
in this case n = 5
=> 2^(8-1) = 2^7 = 128
=> answer is A
The answer is: A | A |
mathematics | A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? | [
"32 kmph",
"33 kmph",
"34 kmph",
"35 kmph",
"36 kmph"
] | A
32 kmph
S = (100 + 300)/45 = 400/45 * 18/5 = 32
The answer is: A | A |
mathematics | A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 12 feet tall and 3 feet in circumference? | [
"9 feet",
"12 feet",
"13 feet",
"15 feet",
"18 feet"
] | total circuit=12/4=3
total feet squirrel travels=3*3=9 feet
ANSWER:A
The answer is: A | A |
mathematics | 210 reputed university students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many o... | [
"25",
"40",
"50",
"60",
"75"
] | We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students... | B |
mathematics | John borrowed 3 soccer boots from Jake, and forgot them on the field, if peter came across a total of 15 boots on the field Jake's boots inclusive, and he took 4 boots at random, what is the probability that Jake's boots were not amongst the 4 taken?. | [
"12/91",
"3/15",
"12/15",
"33/91",
"3/91"
] | Since Jake owns 3 of the boots, the subset from which the 4 boots should be chosen are the 12 boots not owned by Jake from the universe of 15.
The first boot can be one of the 12 from the 15 with probability 12/15.
The second boot can be one of the 11 from the 14 remaining with probability 11/14.
The third boot can be ... | D |
mathematics | Meera purchased two three items from a shop. Total price for three items is Rs.5200/- She have given Rs. 6000/- What is the balance amount meera got? | [
"650",
"400",
"350",
"800",
"750"
] | Total cost of Items : 5200/-
amount Paid : 6000/-
Balance receivable : 6000 - 5200 = 800/-
Answer is D
The answer is: D | D |
mathematics | A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more thanC. Out of a total profit of Rs. 35,000, A receives? | [
"14700",
"14298",
"23877",
"27297",
"17281"
] | Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (35000 * 21/50 ) = Rs. 14,700.
Answer: A
The answer is: A | A |
mathematics | If I, J and K are digits and 9IJK is a 4-digit number that is divisible by 5, which of the following is a possible product of I, J and K? | [
"23",
"48",
"72",
"25",
"94"
] | Key to this question is to remember the fact that a number divisible by 5 must end with 5 OR 0 (i.e K).
If K had to be 0, product should also be 0 regardless of I and J.
The product is a multiple of 5. Only one answer choice meets the requirement.
Ans D.
The answer is: D | D |
mathematics | The number of meters in EB is equal to the square root of the number of centimeters in EB. What is the length of EB (1 meter=100 centimeters)? | [
"100 meters",
"10 meters",
"100 centimeters",
"10 centimeter",
"1 centimeter"
] | I'd plug in the options for this question.
Check option A: if the number of meters in EB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.
Answer: A.
The answer is: A | A |
mathematics | Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 3x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes? | [
"3 minutes",
"4 minutes",
"4.2 minutes",
"6 minutes",
"12 minutes"
] | Rate = Work / Time
Given Rate of Machine A = X / 10 min
Machine B Produces 3x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .
Rate of Machine B = 6x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate... | C |
mathematics | In how many T ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order? | [
"736",
"768",
"792",
"840",
"876"
] | three letters can be arranged in 3! ways.
only one combination EIU is required.
7 letters can be arranged in 7! ways.
thus T=7!/ 3! * 1 = 840.
D
The answer is: D | D |
mathematics | Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 51 years. The age of E is? | [
"45",
"47",
"55",
"49",
"46"
] | Solution
5 years ago average age of A,B,C,D = 45 years
=> 5 years ago total age of A, B, C, D = 45 x 4 = 180 years
=> Total present age of A, B, C, D = 180 + 5x4 = 200 years
If E's present age is x years = 200+x/5= 51
x=55 years. Answer C
The answer is: C | C |
mathematics | If air is called green , green is called blue, blue is called orange, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ? | [
"Orange",
"Sky",
"Water",
"Yellow",
"Black"
] | Explanation:
The colour of clear sky is 'blue' and as given, 'blue' is called 'orange'.
So, the colour of clear sky is 'orange'.
Answer: A
The answer is: A | A |
mathematics | The profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June? | [
"15%",
"32%",
"44%",
"62%",
"80%"
] | Assume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 .
So overall increase is from 100 to 144 is 44%
Answer C
The answer is: C | C |
mathematics | A person travelled from his house to office at 30km/hr and office to house at 15km/hr. Then find the average speed? | [
"15km/hr",
"20km/hr",
"32km/hr",
"24km/hr",
"25km/hr"
] | Average speed = (2*30*15)/(30+15)
= 20km/hr
Answer is B
The answer is: B | B |
mathematics | Sophika can buy watches at a price of P dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of P and X and Y, what is the percent of the markup from her buy price to her sell price? | [
"(YP)/100X",
"100X/(YP)",
"(YP)+100X",
"(YP)-100X",
"(YP)*100X"
] | Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/P *100 = 100X/(YP)
Answer : B
The answer is: B | B |
mathematics | Mukesh borrowed a sum of Rs. 10000 at simple interest from a bank. After two years he takes Rs. 12000 more as loan and discharge all the debt at the end of next 3 years depositing Rs. 27160 to the bank. What is the rate of interest per annum? | [
"5%",
"6%",
"8%",
"10%",
"None of these"
] | si=27160-(principal amount)=27160-22000=5160.
now,(10000*5*R/100) + (12000*3*R/100)=5160.
500R+360R=5160.....Rate=6%.
ANSWER:B
The answer is: B | B |
mathematics | In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability Q that the worker is under 25 years old? | [
"0.30",
"0.25",
"0.45",
"0.70",
"0.90"
] | Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total num... | D |
mathematics | Cindy paddles her kayak upstream at b kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip? | [
"bnp",
"bn/p",
"(b + n)/p",
"bnp/(b + n)",
"pm/n- pn/m"
] | let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/b
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/b)+(d/n)
=d(b+n)/bn
d=pbn/(b+n)=D
The answer is: D | D |
mathematics | Rahul went to a shop and bought things worth Rs. 35, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? | [
"A)19.7",
"B)19.9",
"C)20.9",
"D)21.9",
"E)29.7"
] | Total cost of the items he purchased = Rs.35
Given that out of this Rs.35, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (35−30/100−x)6/100 = 30/100
⇒ 6(35 −0.3 −x) = 30
⇒ (35 − 0.3 − x) = 5
⇒ x = 35 − 0.3 − 5 = 29.7
E)
The answer... | E |
mathematics | A tourist purchased a total of $1,100 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks tha... | [
"$1,430",
"$1,310",
"$1,290",
"$1,270",
"$870"
] | since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value o... | E |
mathematics | The charge for a single room at Hotel P is 20 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ? | [
"15%",
"20%",
"12.5%",
"50%",
"150%"
] | Let rate in R = 100x
then P = 80x
G = 100y
P = 90y
Thus
80 x=90y
or x = 1.125 y
Ans R = 112.5y
so increase = 12.5%
Answer: C
The answer is: C | C |
mathematics | A bowl has only 7 apples and 7 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples? | [
"1/10",
"1/5",
"2/9",
"2/5",
"3/13"
] | 7/14 * 6/13
=3/13
E. 3/13
The answer is: E | E |
mathematics | We have 10 people and 3 chairs. In how many ways chairs can be occupy? | [
"650",
"720",
"810",
"790",
"915"
] | no. of ways they can be occupy = 10*9*8 = 720
Answer is B
The answer is: B | B |
mathematics | How much interest will $10,000 earn in 9 months at an annual rate of 4%? | [
"$300",
"$350",
"$450",
"$550",
"$650"
] | Soln:-
9 months = 3/4 of year;
4% = 4/100=1/25;
$10,000(principal)*1/25(interest rate)*3/4(time)=$300.
ANSWER:A
The answer is: A | A |
mathematics | The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 5: 00 p.m., at what time were there 32 million bacteria in the dish? | [
"11: 00 a.m.",
"8: 00 p.m.",
"6: 00 a.m.",
"8: 00 a.m.",
"10: 00 a.m."
] | Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the ... | A |
mathematics | The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? | [
"18/35",
"18/38",
"18/34",
"18/31",
"18/30"
] | If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35.
Answer:A
The answer is: A | A |
mathematics | Two trains 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? | [
"17.9 sec",
"11.88 sec",
"27.7 sec",
"10.8 sec",
"17.8 sec"
] | Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 190 = 330 m.
Required time = 330 * 9/250 = 11.88 sec.
Answer: B
The answer is: B | B |
mathematics | What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate? | [
"2000",
"2200",
"3000",
"3400",
"3500"
] | A.P.=(200X12900)/[4(200+5X3)]=3000 Ans
Alternative
100+105+110+115=12900
430=12900
100=12900/(430)X100=3000
C
The answer is: C | C |
mathematics | 40% of a number is more than 20% of 650 by 190. Find the number? | [
"227",
"266",
"800",
"277",
"261"
] | (40/100) * X – (20/100) * 650 = 190
2/5 X = 320
X = 800
Answer: C
The answer is: C | C |
mathematics | At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $55,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the c... | [
"$10,000",
"$11,200",
"$12,000",
"$19,800",
"$13,200"
] | 1 machine of type B will cost: 20% down payment of 55,000 = 11,000plusremaining sum (55,000-11,000=44,000) with 40% of finance charges 44,000*1.4=61,600 --> 11,000+61,600=72,600;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000... | D |
mathematics | Evaluate :
28% of 400 + 45 % of 250 | [
"224.8",
"224.9",
"224.5",
"224.6",
"224.1"
] | Explanation:
28% of 400 + 45 % of 250
= (28/100 *400 + 45/100 * 250)
= (112 + 112.5)
= 224.5
ANSWER:C
The answer is: C | C |
mathematics | The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? | [
"10 m",
"16 m",
"245 m",
"19 m",
"27 m"
] | Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: C
The answer is: C | C |
mathematics | Gwen drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 30 miles/hr for the remaining 40 miles of the trip if she made no stops during the trip what was Gwen's avg speed in miles/hr for the entire trip | [
"35",
"20",
"45",
"50",
"55"
] | Avg. speed = total distance / total time
Total distance = 80 miles
Total time = 40 / 15 + 40/30 = 4
Avg. speed = 20.
Answer - B
The answer is: B | B |
mathematics | 40% of the employees in a factory are workers. All the remaining employees are executives. The annual income of each worker is Rs. 390. The annual income of each executive is Rs. 420. What is the average annual income of all the employees in the factory together? | [
"390",
"405",
"408",
"415",
"None"
] | Solution:
Let X be the number of employees.
We are given that 40% of the employees are workers. Now, 40% of X is (40/100)*X =0.4X.
Hence, the number of workers is 2X/5.
All the remaining employees are executives, so the number of executives equals,
(The number of Employees)–(The number of Workers),
= X–(2X/5)
=(3X/5)
T... | C |
mathematics | A student has to obtain 33% of the total marks to pass. He got 92 marks and failed by 40 marks. The maximum marks are? | [
"400",
"300",
"500",
"610",
"175"
] | Let the maximum marks be x
Then, 33% of x = 92+40
33x/100 = 132
x = 400
Answer is A
The answer is: A | A |
mathematics | A family made a down payment of $100
and borrowed the balance on a set of
encyclopedias that cost $400. The
balance with interest was paid in 20
monthly payments of $17.2 each and a
final payment of $3. The amount of
interest paid was what percent of the
amount borrowed? | [
"6%",
"12%",
"14%",
"15.6%",
"20%"
] | interest paid = 17.2*20+3 - 300=47
% off the balance = (47/300) * 100 = 15.67%
Answer is D.
The answer is: D | D |
mathematics | if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr). | [
"18 kmph",
"15.5 kmph",
"12.5 kmph",
"13.5 kmph",
"22.5 kmph"
] | Speed in still water = (16 + 9)1/2 kmph = 12.5 kmph.
answer :C
The answer is: C | C |
mathematics | If 3x−y=27 and 3x+y=243, then find the value of x | [
"1",
"2",
"3",
"4",
"5"
] | Explanation:
3x−y=27=33<=>x−y=3... (i)3x+y=243=35<=>x+y=5... (ii) adding (i) and (ii)=>2x=8=>x=4
Option D
The answer is: D | D |
mathematics | In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes? | [
"430",
"287",
"267",
"262",
"927"
] | Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate
= x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10
= 172 => 4x/10 = 172
=> 4x = 1720 => x
= 430.
Answer:A
The answer is: A | A |
mathematics | Sixteen telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of three members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? | [
"120",
"126",
"252",
"560",
"1260"
] | My ans is 16C3 = 560
D
The answer is: D | D |
mathematics | Two discounts of 40% and 20% equal to a single discount of? | [
"52%",
"48%",
"60%",
"80%",
"70%"
] | {[(100-40)/100]*[(100-20)/100]}%=(60*80)/(100*100)%
=48%
single discount is equal to (100-48)%=52%
ANSWER A 52%
The answer is: A | A |
mathematics | 9 students bought burgers for $143 dollars. If the bill has to be divided among these students, how much amount should be added to the amound to make it
divided amoung them equally in dollars(in whole number of dollars) | [
"$1",
"$2",
"$3",
"$4",
"$5"
] | In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 143 = 8 and 9 is divisible by 9.
Hence, we need to add 1 to this number for it to be divisible by 9
Correct Option: A
The answer is: A | A |
mathematics | In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 12 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture. | [
"12/7",
"4/1",
"2/3",
"3/4",
"3/2"
] | Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+12) = 36/21 = 12/7.
Answer: A.
The answer is: A | A |
mathematics | The radius of the wheel of a bus is 140 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is | [
"125",
"250",
"300",
"330",
"None of these"
] | Radius of the wheel of bus = 140 cm. Then,
circumference of wheel = 2Ï€r = 280Ï€ = 880 cm
Distance covered by bus in 1 minute
= 66â„60 × 1000 × 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 880 cm
∴ Revolutions per minute = 6600000/60×880 = 125
Answer A
The answer is: A | A |
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