Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 06:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# How many factors does the number X have?

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2943
How many factors does the number X have?  [#permalink]

### Show Tags

Updated on: 13 Aug 2018, 02:04
00:00

Difficulty:

5% (low)

Question Stats:

87% (01:04) correct 13% (01:05) wrong based on 154 sessions

### HideShow timer Statistics

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

_________________

Originally posted by EgmatQuantExpert on 27 Feb 2018, 10:08.
Last edited by EgmatQuantExpert on 13 Aug 2018, 02:04, edited 3 times in total.
Retired Moderator
Joined: 07 Jan 2016
Posts: 1090
Location: India
GMAT 1: 710 Q49 V36
Re: How many factors does the number X have?  [#permalink]

### Show Tags

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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2943
Re: How many factors does the number X have?  [#permalink]

### Show Tags

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.
_________________
SVP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1687
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
Re: How many factors does the number X have?  [#permalink]

### Show Tags

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)
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Re: How many factors does the number X have?   [#permalink] 27 Mar 2018, 06:36
Display posts from previous: Sort by