How many factors does the number X have?

Question

e-GMAT Question:

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

Hatakekakashi · Answer

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

EgmatQuantExpert · Answer

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

AkshdeepS · Answer

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)

How many factors does the number X have?

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