Number System (Test 5)

Cat Entrance Exams : Mathematics Or Quantitative Aptitude

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Number System

Number System
| Number System |
Q.1
How many 3 digit numbers are divisible by 6 in all ?
A. 149
B. 150
C. 151
D. 166
Answer : Option B
Explaination / Solution:

Required numbers are 102, 108, 114, ... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then,

a + (n - 1)d = 996

   102 + (n - 1) x 6 = 996

   6 x (n - 1) = 894

   (n - 1) = 149

   n = 150.


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Q.2
A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
A. 10
B. 11
C. 12
D. 15
Answer : Option A
Explaination / Solution:



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Q.3
8597 - ? = 7429 - 4358
A. 5426
B. 5706
C. 5526
D. 5476
E. None of these
Answer : Option C
Explaination / Solution:

7429          Let 8597 - x = 3071
-4358          Then,      x = 8597 - 3071
 ----                       = 5526
 3071
 ----

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Q.4
The smallest prime number is:
A. 1
B. 2
C. 3
D. 4
Answer : Option B
Explaination / Solution:

The smallest prime number is 2.

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Q.5
(12345679 x 72) = ?
A. 88888888
B. 888888888
C. 898989898
D. 9999999998
Answer : Option B
Explaination / Solution:

12345679 x 72= 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888

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Q.6
On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
A. 0
B. 3
C. 5
D. 11
Answer : Option C
Explaination / Solution:

Let x be the number and y be the quotient. Then,

x = 357 x y + 39

  = (17 x 21 x y) + (17 x 2) + 5

  = 17 x (21y + 2) + 5)

Required remainder = 5.


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Q.7
If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
A. 2
B. 5
C. 6
D. 8
E. None of these
Answer : Option E
Explaination / Solution:

Clearly, 4864 is divisible by 4.

So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.

 P = 1.


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Q.8
Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) ?
A. (47 - 43)
B. (47 + 43)
C. (4743 + 4343)
D. None of these
Answer : Option B
Explaination / Solution:

When n is odd, (xn + an) is always divisible by (x + a).

Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).


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Q.9
-84 x 29 + 365 = ?
A. 2436
B. 2801
C. -2801
D. -2071
E. None of these
Answer : Option D
Explaination / Solution:

Given Exp.= -84 x (30 - 1) + 365
= -(84 x 30) + 84 + 365
= -2520 + 449
= -2071

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Q.10
A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
A. 1
B. 2
C. 8
D. 11
Answer : Option A
Explaination / Solution:

Let x = 296q + 75

   = (37 x 8q + 37 x 2) + 1

   = 37 (8q + 2) + 1

Thus, when the number is divided by 37, the remainder is 1.


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