Number System - Study Mode

[#166] $$frac{{768 imes 768 imes 768 + 232 imes 232 imes 232}}{{768 imes 768 - 768 imes 232 + 232 imes 232}} = ?$$
Correct Answer

(A) 1000

Explanation

Solution: Given expression, $$ = frac{{left( {{a^3} + {b^3}}
ight)}}{{left( {{a^2} - ab + {b^2}}
ight)}}$$ xa0 xa0 (where a = 768 and b = 232) $$eqalign{
& = left( {a + b}
ight) cr
& = left( {768 + 232}
ight) cr
& = 1000 cr} $$

[#167] If 6*43 - 46@9 = 1904, which of the following should come in place of * ?
Correct Answer

4

Explanation

Solution: Let 6x43 - 46y9 = 1904 Clearly, y = 3 and x = 5 Hence * must be replaced by 5

[#168] The numbers 2, 4, 6, 8 ..... 98, 100 are multiplied together. The number of zeros at the end of the product must be :
Correct Answer

(C) 12

Explanation

Solution: N = 2 × 4 × 6 × 8 × ..... × 98 × 100 = 2 50 (1 × 2 × 3 × ..... × 49 × 50) = 2 50 × 50! Clearly, the highest power of 2 in N is much higher than that of 5 ∴ Number of zeros in N = Highest power of 5 in N = $$left[ {frac{{50}}{5}}
ight] + left[ {frac{{50}}{{{5^2}}}}
ight]$$ = 10 + 2 = 12

[#169] A number divided by 68 gives the quotient 260 and remainder zero. If the same number is divided by 65, the remainder is :
Correct Answer

(A) 0

Explanation

Solution: Number = (68 × 260) = 17680 On dividing this number by 65, we get zero as remainder

[#170] A man engaged a servant on the condition that he would pay him Rs. 90 and a turban after service of one year. He served only for nine months and received the turban and an amount of Rs. 65. The price of turban is:
Correct Answer

(C) 10

Explanation

Solution: Let the cost of turban be Rs. x According to the question $$frac{{90 + x}}{{12}} = frac{{65 + x}}{9}$$ xa0 xa0 (per month pay) 270 + 3x = 260 + 4x 4x - 3x = 10 x = Rs. 10