subject
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mathematics
|
Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 2 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
|
[
"30",
"20",
"18",
"22",
"6"
] |
21-12 < no of hrs < 21-2
9< no of hrs < 19.
C
The answer is: C
|
C
|
mathematics
|
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
|
[
"18 Kmph",
"17 Kmph",
"72 Kmph",
"18 Kmph",
"16 Kmph"
] |
Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
The answer is: C
|
C
|
mathematics
|
The perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
|
[
"A)72",
"B)45",
"C)729",
"D)34",
"E)35"
] |
Explanation:
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 36/2 = 45 cm2
Answer: Option B
The answer is: B
|
B
|
mathematics
|
If n is an integer and n^4 is divisible by 5, which of the following could be the remainder when n is divided by 5?
|
[
"1",
"2",
"3",
"4",
"5"
] |
option 1
Remainder 1 means 5+1=6
n^4= 6^4= 6*6*6*6/5 is not an integer
option 2
Remainder 2 means 5+2=7
n^4= 7^4=7*7*7*7/5 is not an integer
option 3
Remainder 3 means 5+3=8
n^4= 8^4=8*8*8*8/5 is not an integer
option 4
Remainder 4 means 5+4=9
n^4= 9^4=9*9*9*9/5 is not an integer
option 5
Remainder 5 means 5+5=10
n^4= 10*10*10*10/5 is an integer means n^4 is divisible by 5 if we take n=5
so E is correct
The answer is: E
|
E
|
mathematics
|
If x-1 – 1 is divided by x - 1 the quotient is:
|
[
"1",
"1/(x-1)",
"- 1/(x-1)",
"1/x,",
"– 1/x"
] |
Solution:
x-1 – 1 is divided by (x – 1)
= x-1 – 1 × 1/(x-1)
= 1/x – 1 × 1/(x-1)
= (1 – x/x) × 1/(x-1)
= - (1 – x)/x × 1/(x-1)
= – 1/x [cancel x – 1 from the numerator and denominator].
Answer: E
The answer is: E
|
E
|
mathematics
|
Mike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 20% more than Charlie. Charlie weighs 170% of Mary's weight. Which of these 5 people weighs the highest?
|
[
"Mary",
"Mike",
"Michelle",
"Alan",
"Charlie"
] |
Mary < Michelle < Mike
Charlie < Alan
Let x be Mary's weight.
Mike's weight is 2x and Alan's weight is 1.2*1.7x = 2.04x.
The answer is D.
The answer is: D
|
D
|
mathematics
|
Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
|
[
"66",
"70",
"72",
"75",
"78"
] |
Let the distance one way be x
Time from home to work = x/75
Time from work to home = x/105
Total time = 2 hrs
(x/75) + (x/105)= 2
Solving for x, we get x = 175/2
Time from home to work in minutes= (175/2)*60/75 = 70 minutes
Ans= B
The answer is: B
|
B
|
mathematics
|
How many positive integers less than 5,000 are evenly divisible by neither 18 nor 21?
|
[
"4,514",
"4,475",
"4,521",
"4,428",
"4,349"
] |
integers less than 5000 divisible by 18 5000/18 =333.something , so 333
integers less than 5000 divisible by 21 5000/21 = 238.## , so 238
we have double counted some, so take LCM of 18 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 18 and 21 = 333 +238 -47 =524
now subtract that from 4999. 4999- 524 = 4428 answer D.
The answer is: D
|
D
|
mathematics
|
If b is greater than 1, which of the following must be negative?
|
[
"(2 - b)(b - 1)",
"(b - 1)/3b",
"(1 - b)^2",
"(2 - b)/(1 - b)",
"(1 - b^2)/b"
] |
To be -ive, we should remember it should not be zero apart from being positive...
C will always be 0 or positive..
A and D will be zero at b=2..
B will always be positive..
left is E, where the numerator will always be negative and denominator, a positive..
ans E
The answer is: E
|
E
|
mathematics
|
A third of Arun’s marks in mathematics exceed a half of his marks in English by 20.If he got 360 marks in two subjects together how many marks did he got in English?
|
[
"120,60",
"240,120",
"280,90",
"220,140",
"None of them"
] |
Let Arun’s marks in mathematics and English be x and y
Then (1/3)x-(1/2)y=20
2x-3y=120……>(1)
x+y=360…….>(2)
solving (1) and (2)
x=240
and y=120
Answer is B.
The answer is: B
|
B
|
mathematics
|
If 25% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
|
[
"500",
"600",
"620",
"640",
"660"
] |
We know 25 % people study biology,therefore the no of people not studying = 100 - 25 = 75%
> Therefore the people not studying biology out of a total 880 people are = 75 % of 880
> (75/100)*880 = 660 people
E
The answer is: E
|
E
|
mathematics
|
The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
|
[
"28",
"10",
"288",
"277",
"211"
] |
7*5: 5*x = 7:10
x = 10
Answer: B
The answer is: B
|
B
|
mathematics
|
The greatest number of four digits which is divisible by 10, 16, 24 and 80 is:
|
[
"9000",
"9420",
"9660",
"9840",
"9900"
] |
Greatest number of 4-digits is 9999.
L.C.M. of 10,16, 24 and 80 is 240.
On dividing 9999 by 240, the remainder is 159.
Required number (9999 - 159) = 9840.
Answer: Option D
The answer is: D
|
D
|
mathematics
|
Sam invests $1000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Kody invests $1000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Sam's account, approximately how much more does Kody’s account have?
|
[
"Zero",
"$682.5",
"$68.25",
"$6.825",
"$0.6825"
] |
Sam's interest= $1000*0.12 = $120 or $10 each month.
Kody’s interest, 12%/12 = 1% each month:
For the 1st month = $1000*0.01 = $10;
For the 2nd month = $10 + 1% of 10 = $10.1, so we would have interest earned on interest (very small amount);
For the 3rd month = $10.1 + 1% of 10.1 = ~$10.2;
For the 4th month = $10.201 + 1% of 10.201 = ~$10.3;
...
For the 12th month = $11+ 1% of 11 = ~$11.1.
The difference between Sam's interest and Kody’s interest = ~(0.10 + 0.20 + ... + 1.10) = $6.6.
Answer: D.
The answer is: D
|
D
|
mathematics
|
The avg. age of a group of 24 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
|
[
"22 years",
"23 years",
"24 years",
"25 years",
"27 years"
] |
Total age of 12 students=24*20=480
If total age of 4 students=x
Then, (480+x)/(24+4) =(20+1), x=108
So average age of new students=108/4= 27 years
ANSWER:E
The answer is: E
|
E
|
mathematics
|
When a merchant imported a certain item, he paid a 9 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $76.50, what was the total value of the item?
|
[
"$1,250",
"$1,450",
"$1,650",
"$1,850",
"$2,050"
] |
Let x be the value in excess of $1,000.
0.09x = 76.5
x = $850
The total value was $850 + $1,000 = $1,850.
The answer is D.
The answer is: D
|
D
|
mathematics
|
how many different digit number are there which have digit 1,2,3,4,5,6,7,8, such that digit 1 appears exactly once ?
|
[
"4C1 * 7^2",
"4C1 * 7^3",
"4C1 * 7^4",
"4C1 * 7^5",
"4C1 * 7^6"
] |
Digit 1 can appear in any of the 4 positions of a 4 digit number => 4C1
Further,as repetition is allowed,the othe three digits can have any of the remaining 7 numbers
So total no of different 4 digit numbers possible = 4C1 * 7 * 7 *7 = 4C1 * 7^3
ANSWER:B
The answer is: B
|
B
|
mathematics
|
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by five when k is any of the following values EXCEPT
|
[
"-4",
"-2",
"2",
"-1",
"5"
] |
We have the product of 3 integers: (x-1)x(x-k).
Note that the product of 3 integers is divisible by 5 if at least one multiple is divisible by 5. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 5 these numbers must have different remainders upon division by 5, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 5.
Next, if k=2 then we'll have (x-1)x(x-k)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 5. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 5.
Answer: C.
The answer is: C
|
C
|
mathematics
|
A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,588.25. How many boxes of plain cookies did she sell?
|
[
"0",
"233",
"500",
"695",
"786"
] |
Let #plain cookies sold be X then #chocolate cookies = (total cookies-X)
Equating for X
(0.75)*X +(1.25)*(1585-X)=1588.25
=>x=786
First get the difference of the revenue to the number of boxes.
1588.25-1585=3.25
Now you know that the difference between plain cookies boxes and chocolate cookies boxes is small.
We now divide the revenue by two.
1588.25/2=~794
Because the difference between the possible answers is big, this leaves us with choice E.
The answer is: E
|
E
|
mathematics
|
Each of the integers from 3 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
|
[
"3",
"4",
"5",
"6",
"7"
] |
Answer is 4. In the worst case, you could end up drawing 3,4,5. 7th draw will result in either of 6,7,8,9 which would result in the numbers adding to 10.
B
The answer is: B
|
B
|
mathematics
|
A train 210 m long, running with a speed of 63 km/hr will pass a tree in?
|
[
"18 sec",
"16 sec",
"76 sec",
"12 sec",
"17 sec"
] |
Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 210 * 2/35 = 12 sec
Answer:D
The answer is: D
|
D
|
mathematics
|
There are 6 orators A, B, C, D, E, F. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
|
[
"6! / 3!",
"8! / 6!",
"5! x 3!",
"8! / (5! x 3!)",
"8! / (5! x 4!)"
] |
Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.
The remaining 3 people have to be arranged in 3 places.
Thus, 6C3 x 3! = 6! / 3!
ANSWER:A
The answer is: A
|
A
|
mathematics
|
If the terms of a series are either2or24and the sum of all the terms B of the series is 124, then which of the following could be the number of2sin the series?
|
[
"26",
"29",
"35",
"40",
"48"
] |
Ans: A
Solution: we are not certain how many 2 or 24 are there. but as given sum of all the terms B is 124 means 24*5= 120 so number of 24 can't be more than 5
so 24x +2y = 124
24*5 + 2y =124 then y=2
24*4 + 2y = 124 then y=14
24*3 +2y = 124 then y= 26
24*2 +2y =124 then y = 38
24 +2y = 124 then y= 50
26 is the ans.A
The answer is: A
|
A
|
mathematics
|
Find the area, diameter = 9 m.
|
[
"63.00 square meter",
"63.64 square meter",
"63.08 square meter",
"63.24 square meter",
"63.43 square meter"
] |
Diameter = 9 meter.
Radius = diameter/2.
= 9/2.
= 4.5 meter.
Area of a circle = πr2.
Here, pi (Ï€) = 3.14 meter, radius (r) = 4.5.
Area of a circle = 3.14 × 4.5 × 4.5.
= 3.14 × 20.25.
= 63.64 m2. ANSWER : B
The answer is: B
|
B
|
mathematics
|
A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
|
[
"7",
"9",
"10",
"12",
"14"
] |
Explanation:
7 * 8 : 9 * x = 8:9 => x= 7
A)
The answer is: A
|
A
|
mathematics
|
In a lottery, there are 11 prizes and 55 blanks. A lottery is drawn at random. What is the probability of getting a prize?
|
[
"1/2",
"1/4",
"1/6",
"1/8",
"1/10"
] |
P(winning a prize) = 11 / (11+55) = 11/66 = 1/6
The answer is C.
The answer is: C
|
C
|
mathematics
|
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
|
[
"287 m",
"350 m",
"187 m",
"197 m",
"186 m"
] |
Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x
= 350 m.
Answer: B
The answer is: B
|
B
|
mathematics
|
Of the employees in a company, 40 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?
|
[
"54%",
"52%",
"50%",
"51%",
"55%"
] |
Let E be total no. of employees and F be total no of female employees.
Question asked what is F/E X 100%?
No. of female employees with Masters = 0.4 x E (From the question)
No. of female employees without masters = 0.2 x F (From the question)
Therefore No. of female employees with masters = F - 0.2 F = 0.8 F
The 2 expressions equal each other therefore 0.8F = 0.4E; F/E = 0.4/0.8 = 50%
Ans: C
The answer is: C
|
C
|
mathematics
|
What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
|
[
"2000",
"2300",
"3000",
"3300",
"3400"
] |
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
|
How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?
|
[
"16",
"27",
"31",
"32",
"64"
] |
The solution offered counted it differently.
So I just want to clear it up whether I am also thinking in the right direction.
Number of subset
Since we have 5 digits other than 0, we can take any numbers from the set of 5 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
5c1+5c2+5c3+5c4+5c5=31
And one set is the NULL set having no elements in it so
31+1=32
ANSWER:D
The answer is: D
|
D
|
mathematics
|
A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
|
[
"282",
"3120",
"8383",
"8383",
"3284"
] |
Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
The answer is: B
|
B
|
mathematics
|
Look at this series: 70, 71, 76, __, 81, 86, 90, 91, ... What number should fill the blank?
|
[
"70",
"71",
"80",
"96",
"84"
] |
70,71,76
80,81,86
90,91,96
ANSWER:C
The answer is: C
|
C
|
mathematics
|
A train running at certain speed crosses a stationary engine in 20 seconds. To find out the speed of the train, which of the following information is necessary:
|
[
"Only the length of the train",
"Only the length of the engine",
"Either the length of the train or the length of the engine.",
"Both the length of the train and the length of the engine.",
"none of these"
] |
Explanation:
Since the sum of the length of the train and the length of the engine is needed, so both the lengths must be known.
Correct Option : D
The answer is: D
|
D
|
mathematics
|
A sum fetched a total simple interest of 4043.25 at the rate of 9 %.p.a. in 5 years. What is the sum?
|
[
"5768",
"8985",
"2345",
"6474",
"8723"
] |
Principal = (100 x 4043.25)/(9 x 5)
= 404325/45
= 8985.
ANSWER B
The answer is: B
|
B
|
mathematics
|
There are 10 dozen mangoes in a box. If there are 36
such boxes, how many mangoes are there in all the
boxes together?
|
[
"516",
"3096",
"6192",
"628",
"4320"
] |
Number of mangoes = 12 dozens
= 12 × 10 = 120
∴ Number of mangoes in 36 boxes
= 36 × 120 = 4320
Answer E
The answer is: E
|
E
|
mathematics
|
S, T and U are inner angles in a triangle. If S= T+ U, what can't be the size of T?
|
[
"960 DEGREES",
"9770 DEGREES",
"9570 DEGREES",
"940 DEGREES",
"90 DEGREES"
] |
Given S= T+ U, and S, T and U are inner angles in a triangle. Thus S+ T+ U= 180
T+ U+ T + U= 180 => 2(T+ U) = 180 => T+ U= 90. Thus beta will be less than 90.
Hence the answer is E.
The answer is: E
|
E
|
mathematics
|
How many of the integers between 20 and 80 are even ?
|
[
"21",
"30",
"11",
"10",
"9"
] |
Number start between 20 to 80 is 60 numbers
half of them is even..which is 30
ANSWER:B
The answer is: B
|
B
|
mathematics
|
Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 62 percent of those who attended the meeting were stockholders and 45 percent were employees, what percent were stockholders who were not employees?
|
[
"34%",
"38%",
"45%",
"53%",
"55%"
] |
Let M represent the number of meeting attendees. Then, since 62% of M or 0.62M
were stockholders and 47% of M or 0.45M were employees, it follows that 0.62M +
0.45M = 1.07M were either stockholders, employees, or both. Since 1.07M exceeds
M, the excess 1.07M − M = 0.07M must be the number of attendees who were both
stockholders and employees, leaving the rest 0.62M − 0.07M = 0.55M, or 55%, of
the meeting attendees to be stockholders but not employees.
The correct answer is E.
The answer is: E
|
E
|
mathematics
|
In a question on division with zero remainder, a candidate took 12 as divisor instead of 20. The quotient obtained by him was 25. The correct quotient is?
|
[
"A)15",
"B)24",
"C)28",
"D)29",
"E)30"
] |
Number = (25 * 12) = 300
Correct quotient = 300/20 = 15
A)
The answer is: A
|
A
|
mathematics
|
At present, the ratio between the ages of Arun and Deepak is 4:5. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
|
[
"17 years",
"15 years",
"18 years",
"12 years",
"25 years"
] |
Let the present ages of Arun and Deepak be 4x and 5x years respectively.
Then, 4x + 6 = 26 => x
= 5
Deepak's age
= 5x
= 25 years.
Answer:E
The answer is: E
|
E
|
mathematics
|
On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders R will be:[/b]
|
[
"3, 3, 2",
"3, 4, 2",
"5, 4, 3",
"R=5, 5, 2",
"6, 4, 3"
] |
Let the original number be X. Then by the successive dividing we have followings :
X=5A+2
A=7B+3
B=8C+4.
So we have A=7*(8C+4)+3=7*8C+31, and X=5*(7*8C + 31)+2 = 5*7*8C + 157.
Now by dividing X by 8, 7, 5 successively we have followings :
X=8*(5*7C+19)+5
5*7C+19=7*(5C+2) + 5
5C+2=5C+2.
The remainders are, therefore, 5, 5, 2.
The answer is (D).
The answer is: D
|
D
|
mathematics
|
On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 7 is how many times as great as the frequency corresponding to a reading of 2?
|
[
"40",
"50",
"10^4",
"10^5",
"10^6"
] |
If Richter scale reading goes from X-1 to X it will be 10
if Richter scale reading goes from 2 to 3 it will be 10
if Richter scale reading goes from 3 to 4 it will be 10
if Richter scale reading goes from 4 to 5 it will be 10
if Richter scale reading goes from 5 to 6 it will be 10
Similarly if Richter scale reading goes from 6 to 7 it will be 10
so it will from 2 to 7 i.e 3,4,5,6,7 = 10*10*10*10*10 = 10^5
Answer is D
The answer is: D
|
D
|
mathematics
|
It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 18 minutes, how much time will she spend doing yoga? (rounded to minutes)
|
[
"30 min.",
"41 min.",
"17 min.",
"23 min.",
"25 min."
] |
The ratio is 2:3 = gym:ride, so (18)(3/2) = 27 minutes at the gym, and 27 + 18 = 45 minutes exercise, so (2/3)(45) = 30 minutes yoga.
Answer: A
The answer is: A
|
A
|
mathematics
|
A car owner buys petrol at Rs 7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year ?
|
[
"8.98",
"7.98",
"6.98",
"4.98",
"2.98"
] |
Explanation:
Total quantity of petrol consumed in 3 years = liters
= liters
= liters
Total amount spent = Rs. (3 x 4000) = Rs. 12000.
Average cost = Rs. = Rs. 7.98.
Answer: B
The answer is: B
|
B
|
mathematics
|
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 15% greater than any other employee, what is the lowest possible salary that any one employee earned?
|
[
"$40,000",
"$41,667",
"$42,000",
"$43,750",
"$60,000"
] |
Employee 1 earned $x(say)
Employee 2 will not earn more than $1.15x
Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 20 employees
(1.15x*20)+x=1,050,000
Solving for x=$43,750
Answer D
The answer is: D
|
D
|
mathematics
|
Find the number, difference between number and its 3/5 is 50.
|
[
"110",
"125",
"120",
"140",
"145"
] |
No = x
then x-3/5x = 50
(2/5)x = 50==> 2x=50*5
x = 125
ANSWER B
The answer is: B
|
B
|
mathematics
|
Jamboree and GMAT Club Contest Starts
QUESTION #10:
How many words (with or without meaning)R can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
|
[
"660",
"600",
"500",
"300",
"240"
] |
In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical. in this case,R if you think logically, A,B,C,D options are not divisible by 6!. 6 is total number of letters in the word SELFIE. Only option E is divisible by 6!. So correct answer is E that is 240
The answer is: E
|
E
|
mathematics
|
A chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes forty minutes and 1.5 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?
|
[
"2/7",
"3/10",
"5/11",
"6/13",
"7/15"
] |
The rate of the basic system is 1 room/ (2/3 of an hour) = 3/2 rooms per hour
The rate of the advanced system is 1/1.5 = 2/3 of a room per hour
The combined rate is 13/6 rooms per hour.
The time to ventilate one room is 6/13 of an hour.
The answer is D.
The answer is: D
|
D
|
mathematics
|
Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars 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 1500 jars?
|
[
"m/(m + n)",
"n/(m + n)",
"mn/(m + n)",
"mn/(m – n)",
"mn/(n – m)"
] |
“Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars 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 1500 jars? ”
Since the number “1500 jars” appears over and over, let’s arbitrarily say 1500 jars = 1 lot, and we’ll use units of lots per hour to simplify our calculations.
P’s individual rate is (1 lot)/(m hours) = 1/m. The combined rate of P & Q is (1 lot)/(n hours) = 1/n. We know
(P’s rate alone) + (Q’s rate alone) = (P and Q’s combined rate)
(Q’s rate alone) = (P and Q’s combined rate) – (P’s rate alone)
(Q’s rate alone) = 1/n – 1/m = m/ (nm) – n/ (nm) = (m – n)/(nm)
We now know Q’s rate, and we want the amount of 1 lot, so we use the “art” equation.
1 = [(m – n)/ (nm)]*T
T = (mn)/(m – n)
Answer = D
The answer is: D
|
D
|
mathematics
|
John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 2% and the mobile phone at a profit of 10%. Overall how much he make a profit.
|
[
"s. 90",
"s. 120",
"s. 200",
"s. 250",
"s. 500"
] |
Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 2/100) = 15000 - 300
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -300 + 800 = Rs. 500
As this is positive, an overall profit of Rs. 200 was made.
E
The answer is: E
|
E
|
mathematics
|
A man being asked how much he gave for his watch, replied; If you multiply the price by 4, and to the product add 70, and from this sum subtract 50, the remainder will be equal to 220 dollars.
|
[
"40",
"50",
"60",
"70",
"None of these"
] |
Solution
Let the price of the watch be represented by x
This price is to be multiplied by 4, which makes 4x
To the product, 70 is to be added, making 4x + 70
From this, 50 is to be subtracted, making 4x + 70 - 50
Here we have a number of the conditions, expressed in algebraic terms; but have as yet no equation. We must observe then, that by the last condition of the problem, the preceding terms are said to be equal to 220.
We have, therefore, this equation 4x + 70 - 50 = 220
Which reduced gives x = 50.
Here the value of x is found to be 50 dollars, which is the price of the watch.
Answer B
The answer is: B
|
B
|
mathematics
|
The perimeter of a square is 24 m. Find the area of the square.
|
[
"161 m².",
"36 m².",
"46 m².",
"169 m².",
"33 m²."
] |
Perimeter of square = 24 m
But perimeter of square = 4 × side
Therefore, 4 × side = 24 m
Therefore, side= 24/4 m = 6m
Now, the area of the square = (side × side)
Therefore, area of the square = 6 × 6 m² = 36 m².
ANSWER : OPTION B
The answer is: B
|
B
|
mathematics
|
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 5 cm.
|
[
"187 cm2",
"185 cm2",
"85 cm2",
"85 cm2",
"95 cm2"
] |
Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (5) = 95 cm2
Answer: Option E
The answer is: E
|
E
|
mathematics
|
What is 2 3/4 - 1 2/5 divided by 2/3 - 1/3 ?
|
[
"17/36",
"36/17",
"7/6",
"27/20",
"51/44"
] |
2 3/4 - 1 2/5 = 11/4 - 7/5 = (55 - 28 )/20 = 27/20
2/3 - 1/3 = (6-3)/3 = 3/3 = 1
So 27/20/1 = 27-20
Answer - D
The answer is: D
|
D
|
mathematics
|
Find out the two signs to be interchanged for making following equation correct
5 + 3 x 8 - 12 / 4 =3
|
[
"7",
"3",
"4",
"5",
"6"
] |
Explanation:
On interchanging - and /, we get the equation as
5 + 3 x 8 / 12 - 4 = 3
or 5 + 3 x (2/3) - 4 = 3
or 3 = 3, which is true.
Answer: B
The answer is: B
|
B
|
mathematics
|
On a map, 7 centimeters represents 35 kilometers. Two cities 245 kilometers apart would be separated on the map by how many centimeters?
|
[
"15",
"37",
"49",
"110",
"180"
] |
1 centimeter represents 5 kilometers ( 35/7 )
X=245/5= 49
Answer: C
The answer is: C
|
C
|
mathematics
|
A vessel of capacity 45 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
|
[
"28.8",
"72.9",
"38.3",
"78.3",
"79.3"
] |
Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]^n * T
For the given problem, T = 45, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(45 - 9)/45]^2 (45) = 28.8 litres.
Answer: Option A
The answer is: A
|
A
|
mathematics
|
Ramesh spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%.Find the percentage increase in his savings
|
[
"30%",
"35%",
"40%",
"45%",
"50%"
] |
Let the original income=Rs.100 . Then , expenditure=Rs.75 and savings =Rs.25
New income =Rs.120 , New expenditure =
Rs.((110/100)*75)=Rs.165/2
New savings = Rs.(120-(165/2)) = Rs.75/2
Increase in savings = Rs.((75/2)-25)=Rs.25/2
Increase %= ((25/2)*(1/25)*100)% = 50%.
ANSWER E
The answer is: E
|
E
|
mathematics
|
In a company 10% of male staff are same in number as 1/4th of the female staff. What is the ratio of male staff to female staff
|
[
"3 : 2",
"5 : 2",
"2 : 1",
"4 : 3",
"1 : 2"
] |
10% of MS = 1/4th of FS
-> 10MS/100 = 1/4FS
-> MS = 5/2 FS
:. MS/FS = 5/2 = MS : FS = 5 : 2
ANSWER:B
The answer is: B
|
B
|
mathematics
|
Forty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
|
[
"60",
"70",
"100",
"120",
"140"
] |
40% of the members have passed the test, thus 60% have not passed the test.
We also know that 30+12=42 members have not passed the test, thus 0.6*Total=42 --> Total=70.
Answer: B.
The answer is: B
|
B
|
mathematics
|
How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
|
[
"22 sec",
"77 sec",
"25 sec",
"18 sec",
"17 sec"
] |
D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer:C
The answer is: C
|
C
|
mathematics
|
What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
|
[
"17",
"42",
"46",
"54",
"56"
] |
According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
The answer is: B
|
B
|
mathematics
|
A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 48 lots are to have 100 feet of frontage each, what is the value of x ?
|
[
"5,280",
"3,200",
"3,700",
"4,400",
"4,760"
] |
Total number of plots,be T
Plots with 80ft is (1/9)th of total plots.
Plots with 100ft frontage = (8/9) X total number of plots
i.e 8/9 X T = 48 T = 54
Total lake frontage = 48X100 + 6X80 = 5280
Answer : A
The answer is: A
|
A
|
mathematics
|
One fourth of one third of two fifth of a number is 15. What will be40% of that number
|
[
"140",
"150",
"180",
"200",
"250"
] |
Explanation:
(1/4) * (1/3) * (2/5) * x = 15 then x = 15 * 30 = 450
40% of 450 = 180
Answer: Option C
The answer is: C
|
C
|
mathematics
|
In a factory, each day the expected number of accidents is related to the number of overtime hour by linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported and on another day there were 400 overtime hours logged and 5 accidents. What is the expected number of accidents when no overtime hours are logged?
|
[
"2",
"3",
"4",
"5",
"6"
] |
Explanation :
Let, the number of over time hours be x and expected number of accidents be y.
We will use the equation y = mx + c , where m and c are constant.
Now,according to the question,
if x =1000, then y=8
i.e 8=1000x + c ----(i)
And, if x=400, then y=5
i.e 5=400x + c. ----(ii)
On solving these equations, we get
m=1/200 and c=3.
Hence, in case, no overtime is there i.e x=0, then the number of expected accident will be 3.
Answer : B
The answer is: B
|
B
|
mathematics
|
A’s speed is 30/17 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
|
[
"1/17",
"13/30",
"17/30",
"11/30",
"11/13"
] |
We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 30 meters, B covers 17 meters in that time. So if the race is 30 meters long, when A reaches the finish line, B would be 13 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 13 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 30 meters) would be the same as the time required by B (to cover 17 meters) to reach the finish line.
So B should get a head start of 13/30th of the race.
Answer (B)
The answer is: B
|
B
|
mathematics
|
What sum of money will produce Rs.70 as simple interest in 4 years at 4 1/2 percent?
|
[
"263",
"500",
"388.9",
"368",
"339"
] |
70 = (P*4*9/2)/100
P = 388.9
Answer: C
The answer is: C
|
C
|
mathematics
|
The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 98, what is the difference between the ages of Patrick and Monica?
|
[
"32",
"48",
"45",
"72",
"18"
] |
Ages of P and Mi=3x:5x
Ages of Mi and Mo=3x:5x
Rationalizing their ages. ratio of their ages will be 9x:15x:25x
Sum=49x=98
x=2
Difference if ages of Pa and Mo=25x-9x=16x=16*2=32
Answer A
The answer is: A
|
A
|
mathematics
|
Rs 3600 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part.
|
[
"s 4000",
"s 2800",
"s 1800",
"s 3500",
"s 3100"
] |
Explanation :
Average rate = (144/3600)*100 = 4
Ratio = 1:1
So, first part = (1/2)*3600 = Rs 1800.
Answer : C
The answer is: C
|
C
|
mathematics
|
A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every six leaps of the hare, the jackal takes 7 leaps. Find the ratio of the speed of the hare to the speed of the jackal.
|
[
"64:25",
"8:7",
"5:8",
"25:64",
"6:7"
] |
The hare takes 6 leaps and the jackal takes 7 leaps.
1 hare leap = 4/3 jackal leaps
Thus the hare's 6 leaps = 6*(4/3) = 8 jackal leaps.
The ratio of their speeds is 8:7.
The answer is B.
The answer is: B
|
B
|
mathematics
|
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
|
[
"80",
"89",
"78",
"67",
"56"
] |
Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer: Option B
The answer is: B
|
B
|
mathematics
|
A train covers a distance at a speed of 150kmph in 3 hours. To cover the same distance in 1 hours, it must travel at a speed of?
|
[
"320",
"250",
"560",
"400",
"450"
] |
Distance = 150*3 = 450km
Required speed = 450/1 =450 km/hr
Answer is E
The answer is: E
|
E
|
mathematics
|
Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
|
[
"Rs. 1(2/9)",
"Rs. 2(2/7)",
"Rs. 2(2/11)",
"Rs. 2(2/13)",
"Rs. 2(1/9)"
] |
Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
The answer is: B
|
B
|
mathematics
|
Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow?
|
[
"8000",
"2787",
"27766",
"9976",
"21671"
] |
Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 8160
18x + 45x + 39x = (8160 * 100)
102x = 816000 => x = 8000.
Answer: A
The answer is: A
|
A
|
mathematics
|
Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability E that Jane will be on the same committee as Albert?
|
[
"12%",
"20%",
"33%",
"40%",
"50%"
] |
Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20
No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8
Probability E= (8/20) *100 =40%.
+1 for me.. :D
The answer is: D
|
D
|
mathematics
|
The average earning of amechanic for the first 4days of a week is Rs.32 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
|
[
"s. 10",
"s. 20",
"s. 32",
"s. 40",
"s. 28"
] |
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x 32 + 4 x 22 -20
= Rs. 196
∴ Average earning = 196/ 7
= Rs. 28
E
The answer is: E
|
E
|
mathematics
|
A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
|
[
"5",
"6",
"8",
"4",
"1"
] |
US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A
The answer is: A
|
A
|
mathematics
|
A father divides his estate among his three sons, in such a manner, that:
The first has $1000 less than half of the whole;
The second has 800 less than one third of the whole;
The third has 600 less than one fourth of the whole;
What is the value of the estate?
|
[
"18800",
"28800",
"38800",
"48800",
"None"
] |
Solution
If the whole estate be represented by x, then the several shares will be x/2 - 1000, and x/3 - 800, and x/4 - 600.
And as these constitute the whole estate, they are together equal to x.
We have then this equation x/2 - 1000 + x/3 - 800 + x/4 - 600 = x.
Which reduced gives x = 28800
Proof 28800/2 - 1000 + 28800/3 - 800 + 28800/4 - 600 = 28800
Answer B
The answer is: B
|
B
|
mathematics
|
Find the greatest common factor (GFC) of 24, 40 and 60.
|
[
"1",
"2",
"3",
"4",
"5"
] |
We first write the prime factorization of each given number
24 = 2 × 2 × 2 × 3 = 23*Cubic* × 3
40 = 2 × 2 × 2 × 5 = 23*Cubic* × 5
60 = 2 × 2 × 3 × 5 = 22*square* × 3 × 5
GFC = 22*square* = 4
corect answer is D) 4
The answer is: D
|
D
|
mathematics
|
The sector of a circle has radius of 28 cm and central angle 135o. Find its perimeter?
|
[
"122 cm",
"92.2 cm",
"28.9 cm",
"29.2 cm",
"98.2 cm"
] |
Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 28) + 2(28)
= 66 + 56 = 122 cm
Answer:A
The answer is: A
|
A
|
mathematics
|
If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 3 children have two children of the same sex and one of the opposite sex?
|
[
"1/3",
"2/3",
"1/4",
"3/4",
"3/5"
] |
Let boy be represented by B and girl by G.
The possible outcomes of two children of same sex and one of opposite sex can be:
BBG OR GBB OR BGB OR GGB OR BGG OR GBG
(1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2)
1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 6/8 = 3/4
ANSWER:(D)
The answer is: D
|
D
|
mathematics
|
A bag contains 9 red and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
|
[
"4/7",
"2/3",
"5/8",
"9/14",
"5/7"
] |
Total number of balls = 9+5 = 14
number of white balls = 9
Probability = 9/14
Answer is D
The answer is: D
|
D
|
mathematics
|
If Q= x^4 + y^4 = 100, then the greatest possible value of x is between
|
[
"0 and 3",
"3 and 6",
"6 and 9",
"9 and 12",
"12 and 15"
] |
My attempt:
If Q=x^4+y^4=100, then the greatest possible value of x would be when y is minimum.
Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is B
Hence answer is --
b) 3 and 6.
The answer is: B
|
B
|
mathematics
|
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
|
[
"207",
"209",
"300",
"305",
"307"
] |
We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (24 + 90 + 80 + 15)
=209
ANSWER B
The answer is: B
|
B
|
mathematics
|
Out of 12 employs of a bank, one employ retires and his place, a new employ of age 24 years joins as a result average age of employs reduces by 4 years. The age of the retired employ is:
|
[
"72",
"74",
"78",
"79",
"60"
] |
72
Option 'A'
The answer is: A
|
A
|
mathematics
|
A man gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be:
|
[
"40",
"100",
"120",
"140",
"160"
] |
Let C.P. = Rs. x.
Then, S.P. = Rs. (12% of x) = Rs. 6x/5
New S.P. = 2 * 6x/5 = Rs. 12x/5
Profit = 12x/5 - x = Rs. 7x/5
Profit = 7x/5 * 1/x * 100 = 140%.
ANSWER:D
The answer is: D
|
D
|
mathematics
|
A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
|
[
"28 4⁄7 years",
"31 5⁄7 years",
"32 1⁄7 years",
"27 1⁄2 years",
"None of these"
] |
Required average = (67×2+35×2+6×3/2+2+3)
= (134+70+18/7)=222/7
= 31 5⁄7 years
Answer B
The answer is: B
|
B
|
mathematics
|
Find the sum of 4 digit numbers which are made by 1,2,5,6
|
[
"93424",
"93524",
"92324",
"93324",
"93344"
] |
(n-1)!(1111....)(sum of digits)
(4-1)!(1111)(1+2+5+6)
93324
ANSWER:D
The answer is: D
|
D
|
mathematics
|
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs.2.40 per hour for regular work and Rs.3.20 per hours for overtime. If he earns Rs.432 in 4 weeks, then how many hours does he work for?
|
[
"160",
"175",
"180",
"195",
"185"
] |
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
Therefore, 160 x 2.40 + x x 3.20 = 432
<=> 3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer :B
The answer is: B
|
B
|
mathematics
|
The average of runs of a cricket player of 10 innings was 37. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
|
[
"76",
"81",
"85",
"87",
"89"
] |
Explanation:
Average = total runs / no.of innings = 37
So, total = Average x no.of innings = 37 x 10 = 370.
Now increase in avg = 4runs. So, new avg = 37+4 = 41runs
Total runs = new avg x new no. of innings = 41 x 11 = 451
Runs made in the 11th inning = 451 - 370 = 81 Answer: B
The answer is: B
|
B
|
mathematics
|
an isosceles triangle with sides 13 13 10 and there is a circle inscribed it .find the radius of circle?
|
[
"1.32",
"3.33",
"3.58",
"4.34",
"5.18"
] |
height of triangle = √(13^2 - (10/2)^2) = 12
area of triangle = r * s
where, r = radius of inscribed circle & s=(a+b+c)/2
area of triangle = 1/2 *b*h = 1/2 *10 *12 = 60
s = (13+13+10)/2 = 18
r = area of triangle / s = 60/18 = 10/3 = 3.33
ANSWER:B
The answer is: B
|
B
|
mathematics
|
A man saves Rs 250 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
|
[
"Rs 827.53",
"Rs 862.01",
"Rs 822.02",
"Rs 862.03",
"None of these"
] |
Explanation:
=[250(21/20×21/20×21/20)+250(21/20×21/20)+250(21/20)]=827.53
Option A
The answer is: A
|
A
|
mathematics
|
Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?
|
[
"1/16",
"5/42",
"1/8",
"3/16",
"1/4"
] |
210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;
So, the probability is 2/16=1/8.
Answer: C.
The answer is: C
|
C
|
mathematics
|
8 years ago there were 5 members in the Arthur's family and then the average age of the family was 36 years. Mean while Arthur got married and gave birth to a child. Still the average age of his family is same now. What is the age of his wife at the time of his child's birth was.If the difference between the age of her child and herself was 26 years?
|
[
"16 years",
"26 years",
"36 years",
"66 years",
"86 years"
] |
Since we know that the difference b/w the age of any two persons remains always constant, while the ratio of their ages gets changed as the time changes.
so, if the age of his child be x (presently)
Then the age of wife be x + 26 (presently)
Thus the total age = x + ( x + 26) = 32 [\inline \because 252-220 =32]
Rightarrow x = 3
age of her child is 3 years and her self is 29 years. Hence her age at the time of the birth of her child was 26 years.
Answer: B
The answer is: B
|
B
|
mathematics
|
A circular rim 21 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
|
[
"48pi/x",
"75x",
"48x",
"45x",
"x/75"
] |
Let's try the explanation. We have two wheels. One with 21pi and the other one with 35pi. They have the same speed. In the smaller wheel it's 21pi*x, which must be equal to the speed of the bigger one (35pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 21pi*x=35pi*a.
(21pi*x)/(35pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 45x.
Ans:D
The answer is: D
|
D
|
mathematics
|
Andrew purchased 6kg of grapes at the rate of 74 per kg and 9 kg of mangoes at the rate of 59 per kg. How much amount did he pay to the shopkeeper?
|
[
"1000",
"975",
"980",
"1020",
"1080"
] |
Cost of 6 kg grapes = 74 × 6 = 444.
Cost of 9 kg of mangoes = 59 × 9 = 531.
Total cost he has to pay = 444 + 531 = 975
B
The answer is: B
|
B
|
mathematics
|
Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
|
[
"5/32",
"7/64",
"9/64",
"53/512",
"81/512"
] |
The number of ways to select w, x, and y is: 8*8*8=512
The number of ways to choose three different numbers from the set is 8C3=56.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
P(w < x < y) = 56/512 = 7/64
The answer is B.
The answer is: B
|
B
|
mathematics
|
5.02 can be expressed in terms of percentage as
|
[
"5.02%",
"50.2%",
"209%",
"502%",
"None of these"
] |
Explanation:
While calculation in terms of percentage we need to multiply by 100, so
5.02 * 100 = 502
Answer: Option D
The answer is: D
|
D
|
mathematics
|
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
|
[
"298 m",
"279 m",
"827 m",
"150 m",
"165 m"
] |
Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer:D
The answer is: D
|
D
|
mathematics
|
Shepherd Gopal had a curious aptitude for mathematics and he was known around where he lived as the 'Counting Shepherd.
A man passing throughthe meadow one dat saw Gopal grazing a number of sheep and in the course of a short conversation asked him how many of the grazing sheep were his own. Gopal's reply absolutely baffled him, which was as follows:
If you divide my sheep into two different parts, the difference between yhe two numbers will be the same as the difference between their squares. Now figure it out for yourself the number of sheep I own.'
Can you say just how many sheep Gopal had?
|
[
"1",
"2",
"3",
"4",
"5"
] |
A
Shepherd Gopal had one sheep only.
The answer is: A
|
A
|
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