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# Problems on Numbers Questions

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In this question A^B means A raised to the power of B Start with the integers from 1 to 10^2012. Replace each of them by the sum of its digits to get a string of 10^2012 numbers. Keep doing this until you get 10^2012 single digit numbers. Let m be the number of 1's and n be the number of 2's. Then m - n

A1

B2

C3

D0

Explanation:

We divide all the numbers into groups of 9. (1 to 9), (10 to 18).....
Now when we divide each term in the first group by 9, we get 1, 2, 3 ..0 as remainders. Now digit sum is nothing but finding remainder when a number is divided by 9. So the last term, 10^2012 gives remainder 1 when divided by 9. So there is one "1" extra than 2's.

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If one-third of one-fourth of a number is 15, then three-tenth of that number is:

A35

B36

C45

D54

Explanation:

Lets assume number = x
so, 1/4(1/3 x ) = 15
=> x = 180
so three-tenth of that number = 3/10 * 180 = 54

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In a class there are 45 pupil, out of them 12 are in debate only and 22 in singing only. Then how many in both?

A10

B11

C12

D14

Explanation:

Given, total pupil = 45
Debate + Singing = (12 + 22) = 34
The intersection for two (play both games) = (45 - 12 - 22) = 11

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The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60. If the number of visitors on the 1st and 5th days were in the ratio 7:8 then what is the number of visitors on the 5th day of the library?

A46

B64

C55

D66

Explanation:

If number of visitors on 1st, 2nd, 3rd, 4th and 5th day are a, b, c, d and e respectively then
a + b + c + d = 58 * 4 = 232 - - - (i)
b + c + d + e = 60 * 4 = 240 - - - (ii)
Subtracting (i) from (ii)
e - a = 8 - - - (iii)
Given that e : a = 8 : 7
Let e = 8x and a = 7x.
Given, 8x - 7x = 8 => x = 8 - - - (iv)
So a = 56 and e = 64.

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In an examination involving quantitative aptitude and logical reasoning, 65% examinees cleared quantitative aptitude test while 70% cleared logical reasoning test. If 50% examinees passed both the tests, then how many failed in both tests?

A35%

B15%

C30%

D20%

Explanation:

p(AUB)=p(A)+p(B)-p(AnB)
=65+70-50 =85%(the persons who cleard all)
the persons who did not clear any=100-85=15%

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Three jackals Paar, Marr and Taar together have 675 loaves of bread. Paar has got three times as much as Maar but 25 loaves more than Taar. How many does Taar have?

A175

B275

C375

DNone of these

Explanation:

Lets assume maar (M) = x,
So Paar (P) = 3x
as per the question
Taar (T) = (3x-25)

As per the condition
M+P+T = x + 3x + 3x-25 = 675
7x - 25 = 675 => x=100
=> Taar (T) = 275

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If there are 150 babies born every minute, how many babies share the same birth date world wide?

A224000

B216000

C225000

D218000

Explanation:

In order to have same birth date, all the babies must born on the same day(i.e. in 24 hours)
No. of babies born on same day=(Babies born in every minutes)*(No. of minutes in 24 Hours)
=(150)*(24*60) =216000

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martha was supposed to multiply the number of cans sold with the price of one can to ascertain the amount earned by her, Instead of taking 41 as the number of cans , she wrote 14 by mistake . As a result the product went down by 135. What is the other multiplier

A5

B7

C9

D12

Explanation:

Lets assume multiplier = x
So, 41x=14x+135
=> 27x = 135
=> x = 5

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A content manager is working on an excel sheet. She has 6 columns in the sheet- A,B,C,D,E and F. She has to check that no two columns should have the same entry. She can check only 2 columns at a time. How many times will she have to repeat the comparing process to complete the process for the whole file?

A7

B8

C15

D10

Explanation:

Columns- A B C D E F
No. of comparisons for each column from left to right- 5 4 3 2 1 0

5+4+3+2+1+0=15

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The sides of the triangle are in the ratio 1/2:1/3:1/5 and Its perimeter is 155 cm, what is the difference between the largest sides?

A45 cm

B60 cm

C100 cm

D90 cm

Explanation:

Given Trinagle sides ratio = 1/2:1/3:1/5 = 15:10:6
and its perimeter = 155 cm.
So its sids
15/31*155=75 cm.
10/31*155=25 cm.
6/31*155=30 cm.
So, difference between largst side = (75-30) = 45 cm.

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