Code letters X, Y, and Z each represent one digit in the three-digit

Question

Code letters X, Y, and Z each represent one digit in the three-digit prime number XYZ. If both X and Y are even integers, and if the sum of the three digits is 7, how many different three-digit numbers could XYZ represent?

(A) one
(B) two
(C) three
(D) four
(E) five

(A) one
(B) two
(C) three
(D) four
(E) five

Archit3110 · Answer

possible 3 digit numbers which would be prime as per given condition
223; 241 ; 421; 601
option D

gmatcafe · Answer

If XYZ is prime number and the sum of X, Y, and Z is 7, then Z could be 1 or 3.
If Z=1, then possible three-digit numbers are 241, 421 and 601.
If Z=3, then possible three-digit number is 223. 403 is not prime number since it is divisible by 13 and 31.
 Answer is D) four

MathRevolution · Answer

XYZ is a prime number with X and Y even integer and X + Y + Z = 7

Possible combinations:

=> X = Y = 2 and Z = 3 : 223
=> X = 2 , Y = 4 and Z = 1 : 241
=> X = 4 , Y = 2 and Z = 1 : 421
=> X = 6 , Y = 0 and Z = 1 : 601

Answer D

IanStewart · Answer

Two things here:

- The letters here are just letters. I don't know what it could even mean to call them "code letters";

- Testing even modestly large numbers to see if they're prime is an inordinately time-consuming process. To properly verify that, say, 601 is prime, you need to confirm that you can't divide it by any prime up to √601. So you need to check if you can divide 601 by 2, 3, 5, 7, 11, 13, 17, 19 and 23. That's already far more tedious computational work than any GMAT question would ever require, but in this problem, we also need to do a similar amount of work for four other candidate answers (we can quickly rule out 205, but need to check 223, 241, 403, 421), so the GMAT could never ask a question like this.

There's no fast way to tell if a number like 223 or 601 is prime, and memorizing primes that large would never be helpful on a real GMAT question.

Regor60 · Answer

6 candidates, 1 rejected since it ends in 5, the remaining 5 would need to be checked for primality = not a great question

Code letters X, Y, and Z each represent one digit in the three-digit

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GMAT Problem Solving (PS) Questions

Code letters X, Y, and Z each represent one digit in the three-digit

Prep Toolkit

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