Number System - Aptitude MCQ Questions and Solutions with Explanations

Unit digit in the given product = Unit digit in (4¹⁷⁹³ × 5³¹⁷ × 1⁴⁹¹)
Unit digit in 4² is 6 and so the unit digit in (4²)⁸⁹⁶ is 6
∴ Unit digit in 4¹⁷⁹³
= Unit digit in (6 × 4)
= unit digit in 24, which is 4
Unit digit in 5³¹⁷ is 5 and the unit digit in 1⁴⁹¹ is 1
∴ Unit digit in the given product = Unit digit in (4 × 5 × 1), which is 0

Given expression :
= (1234 + 2345 + 4567) - 3456
= (8146 - 3456)
= 4690

(4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴)
= 4⁶¹(1 + 4 + 4² + 4³)
= 4⁶¹ × 85,
Which is divisible by 17

Product of all odd natural numbers less than 5000
$$\eqalign{ & = 1 \times 3 \times 5 \times 7 \times ..... \times 4999 \cr & = \frac{{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times ... \times 5000}}{{2 \times 4 \times 6 \times 8 \times ... \times 5000}} \cr & = \frac{{5000!}}{{{2^{2500}}\left( {1 \times 2 \times 3 \times 4 \times ... \times 2500} \right)}} \cr & = \frac{{5000!}}{{{2^{2500}} \times 2500!}} \cr} $$

Given expression:
= 38649 - (1624 + 4483)
= (38649 - 6107)
= 32542

Let P = n (n + 1) (n + 2) (n + 3)
Then, n = 1 gives
P = (1 × 2 × 3 × 4) = 24
Hence, the required number is 24

B > A ⇒ A < B ⇒ (A - B) < 0
Since A and B are both positive integers, we have (A + B) > 0 and AB > 0
If (A = 1 and B = 2), we have AB < (A + B)
If (A = 2 and B = 3), we have (A + B) < AB
Thus, we cannot say which one of A + B and AB has the highest value.

11, 111, 1111, 11111,.....
Let m = 2 ⇒ 4 × 2 + 3 = 11
m = 27 ⇒ 4 × 27 + 3 = 111
Each number can be expressed in the form (4m + 3) where m is a natural number.
Hence, statement 1 is only correct.

Let 74844 ÷ x = 54 × 63
Then, $$\frac{74844}{x}$$ = 54 × 63
⇒ x = $$\frac{74844}{54 × 63}$$
⇒ x = $$\frac{8316}{6 × 63}$$
⇒ x = $$\frac{1386}{63}$$   = $$\frac{198}{9}$$
⇒ x = 22

Let the required digit be x
Then,
⇒ x + 1x + 2x + x3 + x1 = 21x
⇒ x + 10 + x + 20 + x + 10x + 3 + 10x + 1 = 200 + 10 + x
⇒ 22x = 210 - 34 = 176
⇒ x = 8
Hence, the required digit is 8