Problem Solving

This problem is from Princeton Review

if a<=6 and a>=-5, then which of the following must be true for all values of a?

a) a<=5
b) a>=-6
c) a<= -5
d) -6<=a<,5
e) none of the above

My answer is E
but solution is B

I don't get why it's B.
Since a>=-6
so A could be -6 which is false because a>=-5


thanks

torofish wrote:This problem is from Princeton Review

if a<=6 and a>=-5, then which of the following must be true for all values of a?

a) a<=5
b) a>=-6
c) a<= -5
d) -6<=a<,5
e) none of the above

My answer is E
but solution is B

I don't get why it's B.
Since a>=-6
so A could be -6 which is false because a>=-5


thanks

You're misinterpreting the question.

You've read the question as "which of the following gives all of the possible values of a?", when in fact the question is "which of the following MUST BE TRUE about a?"

We know that -5 <= a <= 6

Since a MUST be in that range, it MUST BE TRUE that a will always be greater than or equal to -6. In other words, there's no possible value of a that violates (B).

This doesn't mean that a can take every value described in (B); as you pointed out, (B) includes -6, -5.5 and lots of other numbers less than -5. However, every possible value of a fits the range in (B).

Equally correct answers would have been:

a > -1000000
a doesn't equal 53
a < 745.329

For the record, are these types of questions common on the real GMAT?

Stuart Kovinsky wrote:

torofish wrote:This problem is from Princeton Review

if a<=6 and a>=-5, then which of the following must be true for all values of a?

a) a<=5
b) a>=-6
c) a<= -5
d) -6<=a<,5
e) none of the above

My answer is E
but solution is B

I don't get why it's B.
Since a>=-6
so A could be -6 which is false because a>=-5


thanks

You're misinterpreting the question.

You've read the question as "which of the following gives all of the possible values of a?", when in fact the question is "which of the following MUST BE TRUE about a?"

We know that -5 <= a <= 6

Since a MUST be in that range, it MUST BE TRUE that a will always be greater than or equal to -6. In other words, there's no possible value of a that violates (B).

This doesn't mean that a can take every value described in (B); as you pointed out, (B) includes -6, -5.5 and lots of other numbers less than -5. However, every possible value of a fits the range in (B).

Equally correct answers would have been:

a > -1000000
a doesn't equal 53
a < 745.329

@Stuart Kovinsky

I still didn't get your explanation (This might be really dumb, but pls help me)

The Question said "which of the following must be true for all values of a", which according to my thinking is "any value out of range is false"

So my 1st reasoning to this question: Since A is in range of -5 to 6...all the values in that range is true! So with this option C gets canceled right-away!

2nd Reasoning: In Option A, a=5 or less than 5 ( Option A, a<=5) But there is value (A=6) which satisfies the condition of the range. So option A is out! ( There are numbers like -6,-7,-8 till Infinity which satisfy the Option A, but doesn't satisfy the Range Equation)

3rd reasoning: any value below -5 and any value above 6 won't satisfy the range. Option D is out!

Now,
In option B, value of A is greater or equal to -6 (i.e. A can be -6,-5,-4....till infinity) So A= -6 violates the equation range of -5<=A<=6

So my answer is actually E which is wrong according to you and princeton review! so, can you pls comment and rectify my logic if its wrong!

Equally correct answers would have been:

a > -1000000
a doesn't equal 53
a < 745.329

In fact all the alternate answers give by you are Correct, because it hasn't got any "=" sign....

the following options would be wrong:

a=> -1000000 (because in no way a= -1000000)
a<= 745.329 (because in no way a= 745.329)

I think the "Equal or =" sign is making every1 confuse!

vinamra wrote:

Equally correct answers would have been:

a > -1000000
a doesn't equal 53
a < 745.329

In fact all the alternate answers give by you are Correct, because it hasn't got any "=" sign....

the following options would be wrong:

a=> -1000000 (because in no way a= -1000000)
a<= 745.329 (because in no way a= 745.329)

I think the "Equal or =" sign is making every1 confuse!

The equal sign is irrelevant, since it's equal or greater than; the first and third statements would also be correct as you posted.

Let's look at a much simpler question:

If x=5, which of the following MUST be true:

1) x > 3

well yes, if x=5 then it's always greater than 3... must be true.

2) x >= 0

well yes, if x=5 then it's never negative... must be true

3) x <= 1000000

well yes, if x=5 then it's always less than or equal to a million... must be true.

Again, it's all about understanding the question. Saying that it must be true that x is greater than or equal to 0 doesn't mean that it necessarily could be 0, it just means that it's always non-negative.

Here's another non-math example:

If Joe is a human boy, which of the following MUST be true:

1) Joe is not a pig;
2) Joe is either a dog, human, or tree; and
3) Joe is either a boy, girl or rock.

All 3 of those statements MUST be true.

OMG! Now I get it! That was so stupid of me!

BTW Thanks a Million Stuart Kovinsky for helping me out!