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Number System - Aptitude MCQ Questions and Solutions with Explanations

Number System MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Number System with easy and logical explanations. Number System MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-1 section-5

Each section contains 100 MCQs on Number System .
1
Which of the following digits will replace the H marks in the following equation ?
9H + H8 + H6 = 230
Discuss
Answer & Solution
Answer: Option E
Solution:
9H + H8 + H6 = 230
⇒ {(9 × 10) + H} + (10H + 8) + (10H + 6) = 230
⇒ 21H + 104 = 230
⇒ 21H = 126
⇒ H = 6
2
What least number must be added to 1056 to get a number exactly divisible by 23 ?
Discuss
Answer & Solution
Answer: Option A
Solution:
On dividing 1056 by 23, we get 21 as remainder.
∴ Required number to be added = (23 - 21) = 2
3
If a and b are positive integers, a > b and (a + b)2 - (a - b)2 > 29
Then the smallest value of a is -
Discuss
Answer & Solution
Answer: Option B
Solution:
Since (a + b)2 - (a - b)2 = 4ab, So, the given expression should be a multiple of 4
So, the least value of 4ab is 32 and so the least value of ab is 8
Hence, the smallest value of a is 4 and that of b is 2
Hence, a = 4
4
The digit in the unit's place of the number (67)25 - 1 must be -
Discuss
Answer & Solution
Answer: Option B
Solution:
Unit digit of (67)25 = Unit digit of 725
Unit digit of 74 is 1 and so the unit digit of (74)6 is 1
∴ Unit digit of 725 = (1 × 7) = 7
Hence, the unit digit of (725 - 1) is (7 - 1) = 6
5
287 × 287 + 269 × 269 - 2 × 287 × 269 = ?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & \left( {287 \times 287 + 269 \times 269 - 2 \times 287 \times 269} \right) \cr & = {\left( {287} \right)^2} + {\left( {269} \right)^2} - \left( {2 \times 287 \times 269} \right) \cr & = {\left( {287 - 269} \right)^2} \cr & = {\left( {18} \right)^2} \cr & = 324 \cr} $$
[∵ a2 + b2 - 2ab = (a - b)2 ]
6
What number should replace M in this multiplication problem ?
Number System mcq question image
Discuss
Answer & Solution
Answer: Option A
Solution:
Clearly, M = 0,
since 304 × 4 = 1216
7
397 × 397 + 104 × 104 + 2 × 397 × 104 = ?
Discuss
Answer & Solution
Answer: Option B
Solution:
Given expression,
= (397)2 + (104)2 + 2 × 397 × 104
= (397 + 104)2
= (501)2
= (500 + 1)2
= (500)2 + 12 + 2 × 500 × 1
= 250000 + 1 + 1000
= 251001
8
$$\sqrt 2 $$   is a/an -
Discuss
Answer & Solution
Answer: Option C
Solution:
Since, $$\sqrt 2 $$  is a non-terminating and non-repeating decimal, so it is an irrational number.
9
If a number is divisible by both 11 and 13, then it must be necessarily :
Discuss
Answer & Solution
Answer: Option B
Solution:
We know that 11 and 13 are co-prime
So, a number divisible by both 11 and 13 will be divisible by (11 × 13)
10
What is sum of all natural numbers from 1 to 100 ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Required sum
$$\eqalign{ & = \frac{{100}}{2}\left[ {1 + 100} \right] \cr & = 101 \times 50 \cr & = 5050 \cr} $$