If R and S are different integers, both divisible by 5, then which of

Question

If R and S are different integers, both divisible by 5, then which of the following is not necessarily true?

(A) R - S is divisible by 5.
(B) RS is divisible by 25.
(C) R + S is divisible by 5.
(B) R^2 + S^2 is divisible by 5.
(E) R + S is divisible by 10.

Mohammadmo · Answer

5n-5m=5(n-m)✔
5n×5m=25mn✔
5n+5m=5(n+m)✔
(5n)²+(5m)²=25(n²+m²)✔
5n+5m=5(n+m)✖
Option E

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BrentGMATPrepNow · Answer

NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A , because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions (E) R + S is divisible by 10. If R = 5 and S = 10 (both of which are divisible by 5), then R + S = 5 + 10 = 15 Since 15 is NOT divisible by 10, answer choice E is not necessarily true Answer: E Cheers, Brent

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • R and S are different integers, both divisible by 5

To find  
We need to determine
 • From the given options, which one is not necessarily true

Approach and Working out  
Let us assume R = 5a and S = 5b, where a and b are integers

Checking each option individually:
 •  R – S = 5a – 5b = 5 (a – b) , which is always divisible by 5
•  RS = 5a * 5b = 25ab , which is always divisible by 25
•  R + S = 5a + 5b = 5 (a + b) , which is always divisible by 5
•  R^2 + S^2 = 25a^2 + 25b^2 = 5 (5a^2 + 5b^2) , which is always divisible by 5
•  R + S = 5a + 5b = 5 (a + B) , which is divisible by 10   only when   a + b is even, otherwise not

Thus, option E is the correct answer.

Correct Answer: Option E

MathRevolution · Answer

A number is divisible by 5 if the unit digit is either '0' or '5'.

Squaring a number ending with '0' or '5' returns '0' and '5' respectively.

R and S are divisible by 5, so they can be (10, 20) or (15, 25) or ( 10,25) or any other set.

From option A till D, all will satisfy. But for option E: 10 + 25 = 35 is not divisible by 10.

Answer E

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If R and S are different integers, both divisible by 5, then which of

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If R and S are different integers, both divisible by 5, then which of

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