Problem Solving

sanju09 wrote:Which of the following is correct if x is a real number and (x - 11) (x - 3) is negative?
A. x^2 + 5 x + 6 < 0
B. x^2 + 5 x + 6 > 0
C. 5 - x < 0
D. x - 5 < 0
E. 11 - x > 0


[spoiler]Source: https://gmat-math.blocked/2010/02/4gmat[/spoiler]

Once again, this source is unreliable - no question on the GMAT would ever be worded as above.

For example, on the GMAT you'll never see "if x is a real number", because the directions for problem solving and data sufficiency already stipulate that all numbers used on the GMAT belong to the set of real numbers. The GMAT will only mention the relevant types of numbers if a question is more limited (e.g. "if x is an integer" or "if x is positive").

You also won't see a question that asks "which of the following is correct if...".

If this were a GMAT question, the wording would have been:

If (x-11)(x-3) < 0, which of the following must be true?

Sanju's analysis of the two cases is exactly how you should approach the question if you want to solve algebraically. We think: how can the product of two terms be negative? We answer: if one is positive and one is negative. Then we break it down into the two cases as Sanju did, arriving at:

11 > x > 3

Now we look at the choices and ask "which of these is definitely true if the above inequality is true?"

Starting with the 3 simpler choices:

c) 5 < x

Is this a MUST be true? Nope, we could have x=4. Eliminate (c).

d) x < 5

Is this a MUST be true? Nope, we could have x=7. Eliminate (d).

e) x < 11

Is this a MUST be true? Yes! Every possible value of x is less than 11, so (e) is the correct answer.

It's important to realize that "which of the following must be true?" is NOT the same as "which of the following is equivalent to the above?" (e) includes some numbers that aren't in our range, but every number in our range satisfies (e), which is what we need.

One other note: 4, 5, 6, 7, 8, 9 and 10 are not the only possible values for x, since nowhere does it say that x must be an integer.

Kovinsky, you're the man. You just go doo doo on every question here. I love it, haha. Good stuff.

E cann't be an answer. I vote for B

Stuart Kovinsky wrote:

sanju09 wrote:Which of the following is correct if x is a real number and (x - 11) (x - 3) is negative?
A. x^2 + 5 x + 6 < 0
B. x^2 + 5 x + 6 > 0
C. 5 - x < 0
D. x - 5 < 0
E. 11 - x > 0


[spoiler]Source: https://gmat-math.blocked/2010/02/4gmat[/spoiler]

Once again, this source is unreliable - no question on the GMAT would ever be worded as above.

For example, on the GMAT you'll never see "if x is a real number", because the directions for problem solving and data sufficiency already stipulate that all numbers used on the GMAT belong to the set of real numbers. The GMAT will only mention the relevant types of numbers if a question is more limited (e.g. "if x is an integer" or "if x is positive").

You also won't see a question that asks "which of the following is correct if...".

If this were a GMAT question, the wording would have been:

If (x-11)(x-3) < 0, which of the following must be true?

Sanju's analysis of the two cases is exactly how you should approach the question if you want to solve algebraically. We think: how can the product of two terms be negative? We answer: if one is positive and one is negative. Then we break it down into the two cases as Sanju did, arriving at:

11 > x > 3

Now we look at the choices and ask "which of these is definitely true if the above inequality is true?"

Starting with the 3 simpler choices:

c) 5 < x

Is this a MUST be true? Nope, we could have x=4. Eliminate (c).

d) x < 5

Is this a MUST be true? Nope, we could have x=7. Eliminate (d).

e) x < 11

Is this a MUST be true? Yes! Every possible value of x is less than 11, so (e) is the correct answer.

It's important to realize that "which of the following must be true?" is NOT the same as "which of the following is equivalent to the above?" (e) includes some numbers that aren't in our range, but every number in our range satisfies (e), which is what we need.

One other note: 4, 5, 6, 7, 8, 9 and 10 are not the only possible values for x, since nowhere does it say that x must be an integer.

I rejected E just for the sake that it should not turn (x - 11) (x - 3) zero or positive, which is the most important part of the question. I answered [spoiler]B[/spoiler] without checking, as I held in right eliminations only. Can anyone show why [spoiler]B[/spoiler] is correct?

Arcane66 wrote:Kovinsky, you're the man. You just go doo doo on every question here. I love it, haha. Good stuff.

@Arcane66

Aspirants must know how important is this to try questions from a reliable source only, especially when preparing for GMAT. It's the only test known to me that has been absolutely error less in its entire history so far. Experts like Stuart Kovinsky on BTG help us distinguish a genuine GMAT question out of a stock of anything. Everything about the ambiguity in the overall question as discussed by Stuart Kovinsky only reflects GMAT.

Wish you learn and earn both GMAT and respect here on BTG.

Regards

sanju09 wrote:

Arcane66 wrote:Kovinsky, you're the man. You just go doo doo on every question here. I love it, haha. Good stuff.

@Arcane66

Aspirants must know how important is this to try questions from a reliable source only, especially when preparing for GMAT. It's the only test known to me that has been absolutely error less in its entire history so far. Experts like Stuart Kovinsky on BTG help us distinguish a genuine GMAT question out of a stock of anything. Everything about the ambiguity in the overall question as discussed by Stuart Kovinsky only reflects GMAT.

Wish you learn and earn both GMAT and respect here on BTG.

Regards

I don't know what you mean. I was simply complimenting him because he knows how to do any question.

sanju09 wrote:
I rejected E just for the sake that it should not turn (x - 11) (x - 3) zero or positive, which is the most important part of the question. I answered [spoiler]B[/spoiler] without checking, as I held in right eliminations only. Can anyone show why [spoiler]B[/spoiler] is correct?

B is also correct, another reason why this is a horrible question.

x^2+5x+6>0

will be true for all positive values of x. Since we know that 11 > x > 3, B will always hold true.

You're rejecting E because you're misinterpreting the question. Again, the question is NOT "which of the following is equivalent to the above" or "which of the following MAKES the above inequality true"... the question is "IF the above inequality is true, which of the following will also be true".

Here's a simpler example to illustrate:

If x = 3, which of the following must be true?

A) x > 6
B) x > 5
C) x > 4
D) x > 3
E) x > -1000000000000000000000

If x = 3, then x is definitely greater than -1000000000000000000000; accordingly, (E) is the correct answer.

Note that x > -1000000000000000000000 gives us a lot more possible values for x than just 3, but that's not relevant to this particular question.

Stuart Kovinsky wrote:

sanju09 wrote:
I rejected E just for the sake that it should not turn (x - 11) (x - 3) zero or positive, which is the most important part of the question. I answered [spoiler]B[/spoiler] without checking, as I held in right eliminations only. Can anyone show why [spoiler]B[/spoiler] is correct?

B is also correct, another reason why this is a horrible question.

x^2+5x+6>0

will be true for all positive values of x. Since we know that 11 > x > 3, B will always hold true.

You're rejecting E because you're misinterpreting the question. Again, the question is NOT "which of the following is equivalent to the above" or "which of the following MAKES the above inequality true"... the question is "IF the above inequality is true, which of the following will also be true".

Here's a simpler example to illustrate:

If x = 3, which of the following must be true?

A) x > 6
B) x > 5
C) x > 4
D) x > 3
E) x > -1000000000000000000000

If x = 3, then x is definitely greater than -1000000000000000000000; accordingly, (E) is the correct answer.

Note that x > -1000000000000000000000 gives us a lot more possible values for x than just 3, but that's not relevant to this particular question.

Thanks Stuart Kovinsky, I have already got your point through your very first post in this thread and I too agree with your reason why this is a horrible question. But I still cannot put E over B in this particular question, simply because the permissible solution set of B satisfies all needs of 3 < x < 11 without being equivalent to it.

Anyway, it would be so nice of yours if you could please release a translated version of this horrible question so that GMAT wins over its mockers.

Arcane66 wrote:

sanju09 wrote:

Arcane66 wrote:Kovinsky, you're the man. You just go doo doo on every question here. I love it, haha. Good stuff.

@Arcane66

Aspirants must know how important is this to try questions from a reliable source only, especially when preparing for GMAT. It's the only test known to me that has been absolutely error less in its entire history so far. Experts like Stuart Kovinsky on BTG help us distinguish a genuine GMAT question out of a stock of anything. Everything about the ambiguity in the overall question as discussed by Stuart Kovinsky only reflects GMAT.

Wish you learn and earn both GMAT and respect here on BTG.

Regards

I don't know what you mean. I was simply complimenting him because he knows how to do any question.

I never mind spending mind over mindless issues, hope you too won't mind

sanju09 wrote:Which of the following is correct if x is a real number and (x - 11) (x - 3) is negative?
A. x^2 + 5 x + 6 < 0
B. x^2 + 5 x + 6 > 0
C. 5 - x < 0
D. x - 5 < 0
E. 11 - x > 0


[spoiler]Source: https://gmat-math.blocked/2010/02/4gmat[/spoiler]

The correct answer is E. For equation (x - 11) (x - 3) < 0 to be true, either (x-11) or (x-3) needs to be negative.

Case 1: Rejected
x<3, (x-11) is negative, (x-3) is neagtive. Negative X Negative is POSITIVE

CASE 2: CORRECT

3< X < 1 ===> (x-11) is Negative X (x-3) POSITIVE is NEAGTIVE.

Now look at the Answer choice. Only E satisfies this.

Let's also look at another popular answer choice B(INCORRECT)==>
B transforms to (x+3)(x+2) > 0
So either (x+3)>0 && (x+2)>0
OR (x+3) <0 && (x+2)<0

Case 1: (x+3)> 0 and (x+2)>0
x> -3 and x>-2. Final answer ==> x>-2 . This could be -1 -2 -3 .... 12, 13. Some values like 12, 13 do not satify the original condition of (x-11)(x-3)< 0. Hence CASE IS REJECTED

Case 2: (x+3)< 0 and (x+2)<0
x< -3 and x<-2. Final answer ==> x>-3 . This could be -3 -4 -5 ..... Any negtive value of X, does not satify the original condition of (x-11)(x-3)< 0. Hence CASE IS REJECTED.


So the ONLY E is correct.