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# Problems on Numbers Questions

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When numbers are written in base b we have 12*25=333. The value of b is:

A8

B5

C7

D4

Explanation:

Lets assume the base of number = X
Convert all the number to base X
(1*X + 2*X^0)*(2*X + 5*X^0) = (3*X^0 + 3*X^1 + 3*X^2)
By solving the above eq. X=7

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Certain positive integers have these properties:
(I)The sum of the squares of their digits is 50
(II) Each digit is larger than the one to its left.

The product of the digits of the larger integer with both properties is

A7

B36

C25

D48

Explanation:

Integers that exhibit the given properties are 17,1236,345
the largest integer among those is 1236
so product of the digits of 1236 is 36.

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A class of 100 students. 24 of them are girls and 32 are not. Which base am I using?

A0

B6

C2

D3

Explanation:

Let the base be X.
Therefore (X*X + X*0 + 0) = (2*X +4) + (3*X + 2),
=> X * X = 5 * X + 6,
=> X * X - 5 * X -6 = 0,
=> (X- 6) (X+1) = 0
Therefore base is 6.

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Consider the sequence of numbers 0, 2, 2, 4,... Where for n > 2 the nth term of the sequence is the unit digit of the sum of the previous two terms. Let sn denote the sum of the first n terms of this sequence. What is the smallest value of n for which sn >2771?

A692

B693

C694

D700

Explanation:

[0, 2, 2, 4, 6, 0, 6, 6, 2, 8, 0, 8, 8, 6, 4, 0, 4, 4, 8, 2], 0, 2, 2...this series repeats after every 20 terms.

Sum of these 20 terms = 80

So 2771 =34*80 + 51

Sum of 13 terms = 52

So we have to use 34 times 20 terms = 34*20 = 680

680+13 = 693

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Let a, b, c, d and e be distinct integers in ascending order such that(76-a)(76-b)(76-c)(76-d)(76-e) = 1127. What is a + b + c + d

A30

B274

C334

D136

Explanation:

Product of 5 terms equal to 1127. As all the five terms are integers, given product should be a product of 5 numbers. Now factorize 1127.
1127 = 72 * 23 = 7 * 7 * 23
But given that all the a, b, c, d, e are distinct. And we are getting only 3 terms with 7 repeats.
Now the logic is, integers means positive and negative, 7 and - 7 possible and 1, - 1 also possible .
As a,b, c, d, e are in ascending order, the factors should be in decreasing order. So (23, 7, 1, -1, -7)
Now a = 53; b = 69; c = 75; d = 77

a + b + c + d = 274.

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A petri dish hosts a healthy colony of bacteria.once a minute every bacterium divides into two.the colony was founded by a single cell at noon.at exactly 12.43(43 minutes later) the petri dish was half full. At what time the dish will be full?

A12.44

B12.54

C12.45

DNone of these

Explanation:

Given that the bacteria doubles for every one minute,
After 43 minutes it was half full,
It will become full in the next minute i.e. at 12:44 or after 44 minutes

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A calculator has a key for squaring and one for inverting. So if x is the displayed number, then pressing the square key will replace x by x2 and pressing the invert key will replace x by 1/x. If initially the number displayed is 6 and one alternately presses the invert and square key 16 times each, then the final number displayed (assuming no roundoff or overflow errors) will be

A(6^(-2))^16

B(6^(2))^16

C6^32

D632

Explanation:

Even number of inverse key has no effect on the number.
For example, Initially the given number is 6. Square key makes it 6^2 and invert key makes it 1/6^2. Now again square key makes it (1/6^2)^2=1/6^4 and invert key makes it 6^4.
Now observe clearly, after pressing square key 2 times, the power of 6 became 4.
By pressing the square key, the value got increased like 2, 4, 8, .... Which are in the format of 2^n.
So after the 16 pressings the power becomes 2^16
So the final number will be (6^2)^16=6^65536

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In a group of donkeys and pigs, the numbers of legs are 16 more than twice the number of heads. The number of donkeys is

A6

B8

C11

D13

Explanation:

Let the number of donkeys be x and the number of pigs be y.
Then,
=> 4x + 2y = 2(x + y) = 16.
=> 2x + (2x + 2y) = (2x + 2y) + 16.
=> x = 8.

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A Student brought 4 1/3m of yellow ribbon, 61/6 m of red ribbons and 3 2/9m of blue ribbon to decorate his room. How many meters of ribbons didd he buy in all ?

A12 13/18m

B11 13/18 m

C10 13/18m

D13 13/18m

Explanation:

Length of yellow ribbon = 4 1/3 m = 13/3 m
Length of red ribbon = 6 1/6 m = 37/6 m
Length of blue ribbon = 3 2/9 m = 29/9 m
So, the total length of all 3 ribbons = (13/3 + 37/6 + 29/9) = (78+111+58)/18 = (247/18) = 13 13/18 m

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In a group of 15 workers, 5 are good at both Plumping and woodwork, 3 workers are good only at woodwork, and 3 are not good at either of them. How many of them are good at Plumping?

A7

B4

C5

D9

Explanation:

Here is no explanation for this answer

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