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How many factors does the number X have?

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How many factors does the number X have? [#permalink]

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New post Updated on: 07 Mar 2018, 05:46
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C
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Difficulty:

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Question Stats:

95% (00:51) correct 5% (01:11) wrong based on 44 sessions

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e-GMAT Question:



How many factors does the number X have?

1) X is divisible by 47
2) X lies between 100 and 150, inclusive.

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

This is

Question 5 of The e-GMAT Number Properties Marathon




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The next level of the Marathon

[Reveal] Spoiler: OA

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Originally posted by EgmatQuantExpert on 27 Feb 2018, 10:08.
Last edited by EgmatQuantExpert on 07 Mar 2018, 05:46, edited 2 times in total.
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Re: How many factors does the number X have? [#permalink]

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New post 27 Feb 2018, 12:39
EgmatQuantExpert wrote:

Question:



How many factors does the number X have?

1) X is divisible by 47
2) X lies between 100 and 150, inclusive.

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


1) x can be any multiple of 47 = insufficient
2) x can be any number b/w 100 and 500 = insufficient

combining we know that

x is 141

multiple of 47 and 100<x<150

(C) imo
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Re: How many factors does the number X have? [#permalink]

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New post 28 Feb 2018, 10:50

Solution:



Step 1: Analyse Statement 1:
\(X\) is divisible by \(47\).
    • The given statement tells us that\(X\) is a multiple of\(47\).
      o So, from this statement, we can write \(X\)in the form of \(47k\), where \(k\) is any positive integer.
    • To find the number of factors of \(X=47k\), we need to have information on the value of \(k.\)
As we do not have any information on\(k\),
Statement 1 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choices A and D.
Step 2: Analyse Statement 2:
\(X\) lies between \(100\)and \(150\), inclusive.
    • There are \(51\) numbers between \(100\) and \(150\), inclusive.
      o A few of them are prime, few are non-primes, etc.
      o Since we have no information on the type of number, the number of factors of \(X\) cannot be determined uniquely.
Statement 2 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choice B.
Step 3: Combine both Statements:
    • From the first statement, we got \(X=47k\)
    • From the second statement we know that \(X\)lies between \(100\)and \(150\), inclusive.
    • The only number which is of the form \(47k\)and lies between \(100\)and \(150\)is \(141\).
      o \(141 = 47 * 3\)
    • Now that we could derive the number X by combining both the statements given in the question, we can finally calculate the number of factors of X.
      o \(141 = 3*47\)
      o This can be written in the form of \(P1^a * P2^b\), where \(P1\)and \(P2\)are the two primes; a and b are their respective exponents.
         Here, \(P1=3, P2=47, a=1, b=1\).
      o Total factors = \((a+1) * (b+1)\) => \(2*2\)=>\(4\)
By combining both statements we got a unique answer.
Correct Answer: Option C
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Re: How many factors does the number X have? [#permalink]

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New post 27 Mar 2018, 06:36
EgmatQuantExpert wrote:

e-GMAT Question:



How many factors does the number X have?

1) X is divisible by 47
2) X lies between 100 and 150, inclusive.

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

This is

Question 5 of The e-GMAT Number Properties Marathon




Go to

The next level of the Marathon



Simply, If we can find "X", then we can certainly find the factors of "X"

St 1: X is divisible by 47

This list is endless. Insufficient

St 2: X lies between 100 and 150, inclusive.

X can be 105 or 149, we don't know.

Insufficient

Combining we get X = 141.

Sufficient (C)
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Re: How many factors does the number X have?   [#permalink] 27 Mar 2018, 06:36
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