CAT Quantitative Aptitude Questions | CAT Number Systems - HCF and LCM questions

The question is about Sum of the digits. LCM of two numbers is given, we need to find out the sum of digits of the smaller number. A range of CAT questions can be asked based on this simple concept. HCF and LCM from CAT Number Systems is oft tested not just in the context of CAT Number Systems but also inside CAT Quantitative Aptitude questions from other topics. 2IIM has provided fabulous questions with detailed solution for the topic of HCF and LCM in the Free CAT Question bank.

Question 11: LCM of 2 natural numbers p and q where p > q is 935. What is the maximum possible sum of the digits of q?

1. 1
2. 16
3. 8
4. 2

Explanatory Answer

Method of solving this CAT Question from Number Theory - HCF and LCM: Factorize and find product pairs!

We know, 935 = 5*11*17

Let p = hx
q = hy
Where h is the hcf of p and q.
Therefore, lcm of p and q= hxy

We have lcm = 935.
hxy = 935

If h = 1,
Then p = 935
q = 1
Sum of digits of q = 1

If h = 5,
p = 5*17 = 85
q = 5*11 = 55
Sum of digits of q = 10

If h = 11,
p = 11*17 = 187
q = 11*5 = 55
Sum of digits of q = 10

If h = 17,
p = 17*11 = 187
q = 17*5 = 85
Sum of digits of q = 13

HCF can be a combination of 17,11 and 5
If h = 5 * 11,
p = 5 * 11 * 17 = 935
q = 5 * 11 = 55
Sum of digits of q = 10

If h = 5 * 17,
p = 5 * 17 * 11 = 935
q = 5 * 17 = 85
Sum of digits of q = 13

If h = 11 * 17,
p = 11 * 17 * 5 = 935
q = 11 * 17 = 187
Sum of digits of q = 16

Maximum possible sum of digits of q = 16.

The question is "What is the maximum possible sum of the digits of q?"

Hence the answer is "16"

Choice B is the correct answer.