Operation # is defined as: a # b = a² + b² + 2ab, for all non-negative integers. What is the value of (a + b) – 7 when a # b = 196?

A. 5 B. 7 C. 11 D. 13 E. 25

(B) This problem is almost impossible to solve unless we reduce the expression first. From the given information we can safely conclude that: a # b = (a + b)². Now, if we solve the equation:

(a + b)² = 196 (a + b) = 14

Then (a + b) – 7 = 7. The answer is (B).

Notice, that we took the positive square root only since we were restricted to only non-negative integers (as stated in the question), otherwise we could have ended up with two solutions.

Can you please provide another solution to this problem. I do not understand the equations given in the answer.

Post subject: Re: MATH: Test 1, question5 : Symbols

Posted: Thu Apr 29, 2010 11:16 am

Joined: Fri Apr 09, 2010 2:11 pm Posts: 459

The "symbols questions" are the ones where we use some symbol to denote an operation.

In this case we define that a # b equals to a² + b² + 2ab. For any non-negative numbers a and b. (You can think of it as we substitute "a² + b² + 2ab" for "a # b").

Note that (-2) # 3 or (-4) # (-6) are not defined, because we stated that a and b are non-negative numbers.

We are told that a # b = 196. Let us write that in terms of common operations as a # b is defined:

a # b = a² + b² + 2ab = 196

a² + b² + 2ab = 196

So rewriting original questions statement:

We know that a² + b² + 2ab = 196. What is the value of (a + b) – 7 ?

We have two variables in the given equation, so we can not find a not knowing b and vice-versa. But we can see that

a² + b² + 2ab = (a + b)² .

It is a well-known formula. For reference here is how we calculate it: (a + b)² = (a + b) × (a + b) = a × a + a × b + b × a + b × b = a² + 2ab + b².

So we know that (a + b)² = 196

If we denote a + b as x then x² = 196.

x is 14 or -14 and so is a + b. But a + b can not equal to -14 because both a and b are non-negative numbers and therefore the sum of a + b is a non-negative number.

Since we know that a + b = 14 then (a + b) – 7 = 14 - 7 = 7.

Users browsing this forum: No registered users and 1 guest

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.