Problem Solving

For any number y, y* is defined as the greatest +ve even integer less than or equal to y. what is the value of 5.2 - 5.2* ?

1. 0.2
2. 1.2
3. 1.8
4. 2.2
5. 4.0

5.2 - 5.2*
= 5.2 - [Greatest positive even integer =< 5.2]
{the positive integers lesser than or equal to 5.2 are 5, 4, 3, 2 and 1. And what are the positive EVEN integers lesser than or equal to 5.2? 4 and 2}
= 5.2 - [Greater between (4, 2)]
= 5.2 - 4
= 1.2

IMO: B

cypherskull wrote:For any number y, y* is defined as the greatest +ve even integer less than or equal to y. what is the value of 5.2 - 5.2* ?

1. 0.2
2. 1.2
3. 1.8
4. 2.2
5. 4.0

Hi! Wacky symbol questions appear from time to time on the GMAT; these questions almost always resolve to simple substitution.

Of course, before you can substitute you have to understand the question. So, the key to solving these problems is to take the time you need to break down the question stem.

Basically, these are function questions. The question could have read:

for all y, f(y) = the greatest positive even integer less than or equal to y. If y=5.2, what's the value of y - f(y)?

So, we simply plug in:

f(5.2) = greatest positive even integer less than or equal to 5.2 = 4.

5.2 - 4 = 1.2 - choose B!

* * *

As an aside, this question is flawed. To be valid, it should read:

"For all y >=2, y* is defined as the...."

because if y < 2, then there isn't a positive even integer less than or equal to y, rendering the function undefined.

What's the source?

Hi Stuart...got this on the Princeton Review's 2005 edition question bank! Thanks for the explanation.