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# eLitmus Number System Questions eLitmus pH Test Number System

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 1 Given a0 = 1, an = 2an-1(when n is odd) and an = an-1(when n is even), then what is the value of a100-a97-a96 ? A. 0 B. 247 C. 248 D. 249
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Correct answer is : C
Explanation

a99-a97-a96

= 2a98-2a96-a96

= 2a97-3a96

= 4a96-3a96

= a96

= a95

Now, a95 = 2a94 = 2a93

=> a95 = 2a93

and similarly

a93 = 2a91

a91 = 2a89

.

.

.

a5 = 2a3

a3 = 2a1

Multiplying all we get:

a95 = 247a1

=> a95 = 247a0

=>a95 =  247*2

=>a95 = 248

So the required value is: 248

 2 If both 117 and 88 are factors of number a * 47 * 64 * 1313 then what is the smallest possible value of a ? A. 10296 B. 429 C. 99 D. 9
See Answer & Explanation Lets Discuss
Correct answer is : C
Explanation

Writing a * 47 * 64 * 1313 as the product of prime numbers:

a * 47 * 64 * 1313 = a * 47 * 26 * 13 * 101

Writing 117 as product of prime numbers:

117 = 3* 13

Writing 88 as product of prime numbers:

88 = 23 * 11

Since 117 is a factor of a * 47 * 64 * 1313.

=> a * 47 * 64 * 1313/117 will give an integer.

=> a * 47 * 26 * 13 * 101/3* 13 will give an integer

=> a should be a multiple of 32

Similarly since 88 is a multiple of a * 47 * 64 * 1313.

=> a * 47 * 64 * 1313/88 will give an integer

=> a * 47 * 26 * 13 * 101/23 * 11 will give an integer

=> a should be n multiple of 11

Hence from above two, a should a multiple of 9 and 11.

So minimum possible value of a = 9*11 = 99

 3 In a strange twist of hearts, P politician of a country agreed to an average donation of Rs D each. Q of these politicians who had pledged an average of Rs A never donated the pledged money. Which of the following expression represents the percentage of pledged money that was actually donated ? A. 100(PD/QA) B. 100(QA/PD) C. 100-100(QA/PD) D. 100PD-100(QA/PD)
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Correct answer is : C
Explanation

Total donation agreed = PD

Total donation not recieived = QA

Total donation received = (PD-QA)

(PD-QA) is received out of agreed amount PD

So % of agreed amount received = 100*(PD-QA)/PD = 100-100(QA/PD)

 4 The series of differences between consecutive prime numbers is represented as dp1, dp2, dp3, .... dpn .Whare dp1 is the difference between the second and the first prime number. Find the sum of series when n = 23, given that the 23rd prime number is 83 ? A. 81 B. 82 C. 83 D. 87
See Answer & Explanation Lets Discuss
Correct answer is : A
Explanation

We can solve this by writing down all the prime number from 2 to 83 and then finding the differences between them and add them all. This is a tedious task.

Let me introduce you with a shortcut way:

If n was 1.

The series would have been just dp1, which is the difference between the second and the first prime numbers, 3 and 2.

So, dp1 = 3 - 2 = 1

If n was 2.

The series would have been just dp+ dp2

dp2 = difference between 3rd and 2nd odd numbers, 5 and 3 = 5 - 3 = 2

So sum of the series when n is 2 = dp+ dp2 = 1 + 2 = 3

If n was 3.

The The series would have been just dp+ dp2 + dp3

dp3 = difference between 4th and 3rd odd numbers, 7 and 5 = 7 - 5 = 2

So sum of the series when n is 3 = dp+ dp2 + dp3= 1 + 2 + 2= 5

Did you notice something ??

S1 = 1 when last prime number is 3

S2 = 3 when last prime number is 5

S3 = 5 when last prime number is 7 and so on.

So the sum of the series is 2 less than the last prime number.

So S23 = 83 - 2 = 81

 5 How many pairs of positive integers m, n satisfy 1/m + 4/n = 1/12, where n is an odd integer less than 60 ? A. 6 B. 4 C. 7 D. 5 E. 3
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Correct answer is : E
Explanation

1/m + 4/n = 1/12

Since we know something about n, so express m as the value of n.

=> 1/m = 1/12 - 4/n

=> 1/m = (n-48)/(12*n)

=> m = (12*n)/(n-48)

Now since n is odd +ve integers less than 60.

So, n must be greater than 48 so than value of m is +ve.

So range of n is: [49, 59] and only odd numbers.

Hence, n can be: (49,51,53,55,57,59)

From here we can see clearly that for n = 49, 51 and 57, we get positive integer value for m.

So there are 3 possible values for pair (m,n)

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## eLitmus Number System Questions eLitmus pH Test Number System

A collection of questions on Number System for eLitmus Preparation that will help all the eLitmus aspirants in getting a good score in eLitmus pH Test.