If the Number x3458623y is Divisible by 88, What is the Value of x? GMAT Problem Solving

Question: If the number x3458623y is divisible by 88, what is the value of x?

1. 1
2. 2
3. 3
4. 4
5. 5

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

Since x34,586,23y is divisible by 88, which equals 8 times 11, it is also divisible by 8 and 11.

A number must have the last three digits that may be divided by 8, so for example, 23y must be divisible by 8. That is only feasible if y=2 since then 232/8=29. Our number is therefore x34,586,232.

The difference between the sums of the odd-numbered digits (first, third, fifth, etc.) and the even-numbered digits (second, fourth, etc.) must be divisible by 11 for a number to be divisible by 11. As a result, the equation (x+4+8+2+2)-(3+5+6+3)=x-1 must divide by 11, which limits the value of x to 1.

A is the correct answer.

Approach Solution 2:

x3458623y should be divisible by 8 and 11 since it is divisible by 88.
x+14+y -17 = n * 11 n can't be 2, as it would cause the RHS to become 22, and the maximum we can get on the LHS is 9+9-3 = 15.
so n=0 or 1

240 is completely divisible by 8, thus the number that follows that will be no less than 232. Now that it should also be divisible by 8, 23y should also be divisible by 8.
hence, y=2

Now, x+2–3 = n*11, and x–1 = n*11.
Now that lhs max can only be 9-1 = 8, n = 1 is likewise not possible.

hence, n=0 and x=1
A is the correct choice.

“If the number x3458623y is divisible by 88, what is the" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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