Number System - Study Mode

[#586] 136 × 12 × 8 = ?
Correct Answer

12066

Explanation

Solution: = 136 × 12 × 8 = 136 × 96 = 136 × (100 - 4) = (136 × 100) - (136 × 4) = 13600 - 544 = 13056

[#587] The number of digits in the smallest number, which when multiplied by 7 yields all nines, is :
Correct Answer

(D) 6

Explanation

Solution: We keep on dividing 99999..... by 7 till we get 0 as remainder. ∴ Required number = 142857 Number of digit = 6

[#588] Let x = 224 and y = 322. If the highest common factor of 23x and a × y is divisible by x and y, then what can be the possible value of a?
Correct Answer

(D) 16

Explanation

Solution: x = 224, y = 322 ⇒ 23x = 23 × 224 = 23 × 16 × 14 ⇒ ay = 322a = a × 23 × 14 ⇒ If HCF of 23x and ay is divisible by x and y then, 23 × 16 × 14 = a × 23 × 14 a = 16

[#589] The number 334 × 545 × 7p is divisible by 3340 then what is the minimum value of P?
Correct Answer

(A) 2

Explanation

Solution: $$eqalign{
& frac{{334 imes 545 imes 7p}}{{3340}} cr
& Rightarrow frac{{334 imes 545 imes 7p}}{{334 imes 10}} cr
& Rightarrow frac{{109 imes 7p}}{2} cr
& { ext{Go through by options take 2}} cr
& Rightarrow frac{{109 imes 72}}{2} cr
& { ext{So, answer is 2}} cr} $$

[#590] The smallest five digit number which is divisible by 12, 18 and 21 is:
Correct Answer

(A) 10080

Explanation

Solution: We know, smallest five digit number is = 10000 LCM of 12, 18, 21 = 252 Difference = 252 - 172 = 80 Then number is = 10000 + 80 = 10080