2 GMAT Number system question

For the LCM and HCF let me be a little more detailed.
Step 1
Assume numbers to be x and y
Now they must have a 13 in their prime factor boxes to have a 13 in their GCF.

Step 2
If you look at the prime factors of 455 it is composed of 13*7*5
hence x and y should be 13*7 and 13*5

Step 3
Look at the answer choices and look at the constraints in the question. Clearly the answer choices should have 455 as a multiple. The answer choices you are left with are 91 and 65. 65 is automatically disqualified because it is part of the constraints. 91 is the answer

Posted from GMAT ToolKit

Need a little more explanation on the first question.

Posted from GMAT ToolKit

Ilhom1986....I need more explanation in First question.
Answer is not option (e), it's (a)

\(2^{96}+1\) = \(2^{(32)*3} + 1^3\) = \((2^{32}+1)\) * something..

apply \(a^3+b^3\) = \((a+b)(a^2+b^2-ab)\)

hence A

Thanx for explaining...Now it's seems to be a very simple one...

Thanks for the explanation for 1....i was able to answer question 2 but was stuck between b and e for question 1.

what i would have done is this:

i would have changed this number question to a variable based question..

2^32 + 1 = 2^n + 1 assuming n=1 i would get 3.. and 3 is divisilbe by 3 .. now i would change the answer options to variables assume n=1 and see if the ersult is divisible by 3... 32 is n, 16 is n/2, 64 is 2n and so on ...:

1st option: 2^96 + 1 = 2^3n +1 and for n=1 it would be 9 which is divisible by 3.. if u dont have time nd clocks ticking mark it and move ahead!!!

2nd option : 2^16 + 1 = 2^n/2 +1 for n=1 it would be root2 + 1 which is not divisble by 3.

same for option 3:2^64 + 1 = 2^2n +1 for n=1 would be 5 not divisible by 3.. eliminated
same goes for option 5: 14 is nt divisible by 3..


answer is A

this approach can backfire: so assume 2 values and solve it!!

for quetion 2:

product 0f two numbers = lcm * hcf of these numbers

i just need to find product of 13 and 455 and see which number in the options divides this product perfectly..

one thing imp : the product will end in 5.. so u can eliminate option b and d straight up as any integer product with them wont end in 5..
option e is a filler as per the question constraints..

now we have option a and option c.. little calc and the answer is a..