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ksan04
10-03-2003, 12:38 AM
1.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

Ainariel
10-03-2003, 08:52 AM
hi ksan,

I think the answer is E). Since a could be 6 or -5, A and C can be eliminated immediately. I think -6<a<7, which is not a choice here.
What do you think?

Tina

ksan04
10-03-2003, 12:54 PM
Hi Tina

I totally agree with you but as per PR the ans is B

Ainariel
10-03-2003, 03:51 PM
hi ksan,

That's pretty weird, huh? I would have thought that if B) were true, then A) would be also. What do you think?

Tina

boofoo_2003
10-05-2003, 02:03 PM
Hey Guys:

The answer B is correct. Here is why:

B implies that "a" is greater than -6 and since we are given that "a" is greater than -5, it has to be greater than -6 for sure.

A is not correct because even though "a" is given to be less than 6, it is not necessary that "a" is less than 5 - i.e. What if a = 5.5

Hope this helps!!

kuriang
10-05-2003, 02:37 PM
The answer B is correct. Here is why:

B implies that "a" is greater than -6 and since we are given that "a" is greater than -5, it has to be greater than -6 for sure.

Hi boofoo_2003
What about a=10 ? According to option B it is correct(10>=-6)
but according to question stem "a has to be <=6"
So option B is NOT correct.

The trick to this question is to find out the range of 'a'.
We know that 'a' is greater than or equal to -5'
and 'a' is less than or equal to 6'.So any values between
-5 and 6 will be fine for 'a'. Mathematically we can
express this as -5<=a<=6. Since all the options given have
some values outside this range,none of them are correct.
So the ans to this question is E.

lobato
10-09-2003, 01:13 AM
Originally posted by kuriang

The answer B is correct. Here is why:

B implies that "a" is greater than -6 and since we are given that "a" is greater than -5, it has to be greater than -6 for sure.

Hi boofoo_2003
What about a=10 ? According to option B it is correct(10>=-6)
but according to question stem "a has to be <=6"
So option B is NOT correct.

The trick to this question is to find out the range of 'a'.
We know that 'a' is greater than or equal to -5'
and 'a' is less than or equal to 6'.So any values between
-5 and 6 will be fine for 'a'. Mathematically we can
express this as -5<=a<=6. Since all the options given have
some values outside this range,none of them are correct.
So the ans to this question is E.

You can't pick a=10. The problem states that -5<=a<=6. Therefore, you must pick a value of a that falls within this range. Whether you pick -5, 0, 1/8, 5.75, or -2.5, they are all greater than or equal to -6. This holds true for any value of a that falls with in range of -5<=a<=6.

desperateguy
10-09-2003, 02:15 PM
I don't quite understand your explanation and IMHO answer should be E).

In B) you can assume that a=-6 and this number would fall out of the range.

sujayath
10-09-2003, 04:31 PM
Hi,

We cannot assume a=-6. We should take a value that is within the range given in the problem statement and check whether the given choice is true or not. But ainarel/kuriyang/desperateguy assume a value from the given choice and try to check the validity in the question.

If a>=-5 (it is given in the question), itsn't it true that a should be >=-6. I agree, strictly speaking, a>-6 but that doesn't mean a>=-6 is wrong.

lobato
10-09-2003, 11:03 PM
Originally posted by desperateguy

I don't quite understand your explanation and IMHO answer should be E).

In B) you can assume that a=-6 and this number would fall out of the range.

Hmmm. I'm not very good at explaining things but let me try again. I'm going to make an analogy but since I'm a little hungover, it might not be a great analogy. Here it goes:

I'm going to perform a magic trick on you. I would like you to pick a number from 70 to 80. It doesn't need to be an integer. It can be 73.5, 76.4256, 71.33333, 79, or whatever. Did you pick your number? Good. Now I'm going to predict what your number is. Here's my prediction: your number is above 30. Am I correct? Of course. No matter what number you pick, my prediction will be correct. This is essentially what the problem is saying. Any value for "a" you pick that's within the range stipulated by the problem, it will *always* be greater than -6.

Now let met make an analogy of what some of the responses on this thread have said using that same magic trick. I asked you to pick a number between 70 and 80. I then predicted your number is above 30. Then you say to me, "Tell, you're wrong. The number I picked was 14, which is less than 30." But the number you picked violated the range I gave you to begin with. You can't pick 14 because it's not between 70 and 80.

lobato
10-09-2003, 11:07 PM
Oops, typo. The quotation above should read "Well, you're wrong" not "Tell, you're wrong." I guess there's no edit feature on these boards.

dig12us
11-11-2003, 07:59 PM
choice b says a>=-6 which means it could be -6 and it is out of the range so B cannot be the answer it has to be E

ted13ted
11-12-2003, 03:34 PM
lobato is, of course, correct. And I don't know how anyone could possibly explain the rationale any better.