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# GMAT Diagnostic Test Question 4

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CIO
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Re: GMAT Diagnostic Test Question 4 [#permalink]  08 Apr 2010, 03:06
Thank you guys! I've corrected the OE and OA both in the files and in the second post. +1 for both of you.
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Re: GMAT Diagnostic Test Question 4 [#permalink]  16 May 2010, 18:39
This question was hard but I think it makes sense now. And this might be a bonehead question, but when the [X] looks like this, what exactly is the significance to remember? Does it mean it can be both positive and negative? I'm slowly preparing for the math section....not trying to score off the charts just mediocre...

Thanks in advance.
CIO
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Re: GMAT Diagnostic Test Question 4 [#permalink]  17 May 2010, 06:44
Hi Rachel,

Here's a comprehensive guide to absolute values:
math-absolute-value-modulus-86462.html

The most important things to remember about $$|X|$$:

$$|X| \ge 0$$

$$|X| = |-X|$$

Examples:

$$|-3| = 3$$

$$|3| = 3$$

$$|0| = 0$$

Good luck with your GMAT!
Rachcu13 wrote:
This question was hard but I think it makes sense now. And this might be a bonehead question, but when the [X] looks like this, what exactly is the significance to remember? Does it mean it can be both positive and negative? I'm slowly preparing for the math section....not trying to score off the charts just mediocre...

Thanks in advance.

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Intern
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Re: GMAT Diagnostic Test Question 4 [#permalink]  02 Dec 2010, 05:08
Statement 1 clearly states that X!< 5
i.e. X could be 1,2,3,4. So, it is alone insufficient.

But, I didn't understand II statement.
(2) l x l is divisible by 6

can anyone please explain me the concept. And also if possible the concept of absolute value.

Regards,

G
Math Expert
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Re: GMAT Diagnostic Test Question 4 [#permalink]  02 Dec 2010, 05:22
Expert's post
girindra wrote:
Statement 1 clearly states that X!< 5
i.e. X could be 1,2,3,4. So, it is alone insufficient.

But, I didn't understand II statement.
(2) l x l is divisible by 6

can anyone please explain me the concept. And also if possible the concept of absolute value.

Regards,

G

Is $$x$$ a prime integer?

(1) $$x!$$ is not divisible by 5 --> $$x=0$$ (note that $$0!=1$$), $$1$$, $$2$$, $$3$$, or $$4$$. Not sufficient.
(2) $$|x|!$$ is divisible by 6 --> $$|x|>2$$ (if x is an integer more than or equal to 3, than (|x|)! will be divisible by 6, also if x is less than or equal to -3, then (|x|)! will be divisible by 6). Not sufficient.

(1)+(2) $$x=3$$ (prime) or $$x=4$$ (not prime). Not sufficient.

Answer: E.

For absolute values check: math-absolute-value-modulus-86462.html ;
For number theory check: math-number-theory-88376.html

Hope it helps.
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Intern
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Re: GMAT Diagnostic Test Question 4 [#permalink]  16 May 2011, 21:23
I have an issue with the way |X!| is interpreted. Since it is the absolute value of the factorial, and factorial is not defined for negative values hence, possible values of X in (2) could only be positive 3 or 4.

we can consider -3 or -4 only if it's written as |x|!

In any case, even if corrected, E would still be the answer.
Intern
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Re: GMAT Diagnostic Test Question 4 [#permalink]  17 May 2011, 07:29
Well the question reads |X!| and not |X|! (check the pdf)

If a number has a factorial, it is positive.
Intern
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Re: GMAT Diagnostic Test Question 4 [#permalink]  27 Sep 2011, 16:29
how did you guys get that X! < 5? Does not being divisible by 5 make it smaller than it ?
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Re: GMAT Diagnostic Test Question 4 [#permalink]  04 Oct 2011, 03:08
bb wrote:
GMAT Diagnostic Test Question 4
Field: Arithmetic, Factorial
Difficulty: 650
 Rating:

Is $$X$$ a prime integer?

(1) $$x!$$ is not divisible by 5
(2) $$|x|!$$ is divisible by 6

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient

St 1: X! not divisible by 5. so X is less than 5. It could be 1, 2, 3, 4. not sufficient

St 2: X! is divisible by 6. which means X is at least divisible by 1, 2, 3, and 6. So, it is not a prime. Sufficient.

So, my pick is B
Intern
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Re: GMAT Diagnostic Test Question 4 [#permalink]  04 Oct 2011, 03:14
^^ I got the second statement wrong.... understood the explanation from the other posts...
Manager
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Re: GMAT Diagnostic Test Question 4 [#permalink]  28 Oct 2011, 21:41
Ans E

From 1=> options come out to be 1,2,3,4

From 2=> options come out to be 3,4,......

Using both => 3,4

So E.
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Re: GMAT Diagnostic Test Question 4 [#permalink]  26 Apr 2012, 22:39
Ans: E

From 1=> options come out to be 1,2,3,4 hence, x can be a prime number or not a prime number (4 for eg.)

From 2=> options come out to be 3 (prime) ,4 (not prime),......

Hence Ans. is E
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Re: GMAT Diagnostic Test Question 4 [#permalink]  19 Sep 2012, 21:17
both staements we can conclude that answer would be either 3 0r 4..so not sufficient E
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Chennai, India.

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Re: GMAT Diagnostic Test Question 4 [#permalink]  07 Nov 2012, 01:08
Bunuel wrote:
girindra wrote:
Statement 1 clearly states that X!< 5
i.e. X could be 1,2,3,4. So, it is alone insufficient.

But, I didn't understand II statement.
(2) l x l is divisible by 6

can anyone please explain me the concept. And also if possible the concept of absolute value.

Regards,

G

Is $$x$$ a prime integer?

(1) $$x!$$ is not divisible by 5 --> $$x=0$$ (note that $$0!=1$$), $$1$$, $$2$$, $$3$$, or $$4$$. Not sufficient.
(2) $$|x|!$$ is divisible by 6 --> $$|x|>2$$ (if x is an integer more than or equal to 3, than (|x|)! will be divisible by 6, also if x is less than or equal to -3, then (|x|)! will be divisible by 6). Not sufficient.

(1)+(2) $$x=3$$ (prime) or $$x=4$$ (not prime). Not sufficient.

Answer: E.

For absolute values check: math-absolute-value-modulus-86462.html ;
For number theory check: math-number-theory-88376.html

Hope it helps.

Bunuel, aren't |0| !, |1| ! and |2| ! all divisible by 6 as well? Though this fact does not affect the answer here, it can affect at other times. You explain it here too: http://gmatclub.com/forum/if-n-is-a-positive-integer-is-n-3-n-divisible-by-109941.html#p1075285.
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Math Expert
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Re: GMAT Diagnostic Test Question 4 [#permalink]  07 Nov 2012, 04:23
Expert's post
closed271 wrote:
Bunuel wrote:
girindra wrote:
Statement 1 clearly states that X!< 5
i.e. X could be 1,2,3,4. So, it is alone insufficient.

But, I didn't understand II statement.
(2) l x l is divisible by 6

can anyone please explain me the concept. And also if possible the concept of absolute value.

Regards,

G

Is $$x$$ a prime integer?

(1) $$x!$$ is not divisible by 5 --> $$x=0$$ (note that $$0!=1$$), $$1$$, $$2$$, $$3$$, or $$4$$. Not sufficient.
(2) $$|x|!$$ is divisible by 6 --> $$|x|>2$$ (if x is an integer more than or equal to 3, than (|x|)! will be divisible by 6, also if x is less than or equal to -3, then (|x|)! will be divisible by 6). Not sufficient.

(1)+(2) $$x=3$$ (prime) or $$x=4$$ (not prime). Not sufficient.

Answer: E.

For absolute values check: math-absolute-value-modulus-86462.html ;
For number theory check: math-number-theory-88376.html

Hope it helps.

Bunuel, aren't |0| !, |1| ! and |2| ! all divisible by 6 as well? Though this fact does not affect the answer here, it can affect at other times. You explain it here too: http://gmatclub.com/forum/if-n-is-a-positive-integer-is-n-3-n-divisible-by-109941.html#p1075285.

No.
|0|! = 0! = 1;
|1|! = 1! = 1;
|2|! = 2! = 2.
Neither of them is divisible by 6.

Hope it's clear.
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Re: GMAT Diagnostic Test Question 4 [#permalink]  04 Oct 2013, 02:52
bb wrote:
GMAT Diagnostic Test Question 4
Field: Arithmetic, absolute values
Difficulty: 650

Is $$x$$ a prime number?

(1) $$|x|=2$$
(2) $$x^2=4$$

(1) x! is not divisible by 5 --> x=0 (note that 0!=1), 1, 2, 3, or 4. Not sufficient.
(2) |x|! is divisible by 6 --> |x|>2 (if x is an integer more than or equal to 3, than (|x|)! will be divisible by 6, also if x is less than or equal to -3, then (|x|)! will be divisible by 6). Not sufficient.

(1)+(2) x=3 (prime) or x=4 (not prime). Not sufficient.

Answer: E.
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Re: GMAT Diagnostic Test Question 4 [#permalink]  09 Apr 2014, 05:34
Am I the only one who cant see the answer options?
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Re: GMAT Diagnostic Test Question 4 [#permalink]  09 Apr 2014, 05:43
Expert's post
gayanep wrote:
Am I the only one who cant see the answer options?

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.
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Re: GMAT Diagnostic Test Question 4   [#permalink] 09 Apr 2014, 05:43

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