What is the value of the positive integer x? (1) 21x is a multiple of

Question

What is the value of the positive integer x?

(1) 21x is a multiple of 39
(2) 21x < 300

Showmeyaa · Answer

x = ?
1)21x = 39k
x = 39k/21 = 13k/7, where k is an integer.
For k = 7, x = 13
For k = 14, x = 26 - Insufficient!
2)21x < 300
x < 100/7 ~ 14.something
Since, x = int. x<=14 - Insufficient!
Combining (1) & (2):
x = 13
IMO, (C)!

Nidzo · Answer

(1) Gives us some info to limit our scope, but there are infinite possible solutions as it does not supply a range limit.  INSUFFICIENT

(2) Gives us a range, but there are many possible solutions for x.  INSUFFICIENT

(1+2) Together we are given enough to solve for x, but to ensure that there are not multiple options which fit the criteria of x being below 300 and being a multiple of 39, work out the LCM of 21 and 39.

Prime factorising 21: 3 and 7
Prime factorising 39: 3 and 13

LCM = 3*13*7 
= 273

As there is nothing below or above 273 which meets the criteria given, x can only be 13.  SUFFICIENT

Answer C

TestPrepUnlimited · Answer

Statement 1:

21 already has a factor of 3. Then x only needs to be a multiple of 13. Insufficient.

Statement 2:

Insufficient.

Combined:

We know x only needs to be a multiple of 13. The first value is 21*13 = 200+, and the second value is 21*26 > 300, so we cannot have any other values for 21x.

Ans: C

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are asked the value of positive integer  x

Statement 1:   21x is a multiple of 39
  According to this statement,  21x=39k  where k is a positive integer
 ⇒x=\frac{39k}{21} 
 ⇒x=\frac{13k}{7}  
 Since x is a positive integer,  k has to be a multiple of 7  
 For different values of k (7, 14, 21 etc), the value of x will be different (13, 26, 39 etc) 
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:   21x < 300
  Accordign to this statement,  21x < 300 
 ⇒x<\frac{300}{21} 
 ⇒x<\frac{100}{7} 
 ⇒x<14.29  
 We are not getting an exact value of x from this 
 Thus,  statement 2 alone is not sufficient

Combining:   
  From statement 1, for different values of k (7, 14, 21 etc), the value of x will be different (13, 26, 39 etc) 
 From statement 2,  x<14.29  
 The only possible value of x is 13

Hence the right answer is    Option C

What is the value of the positive integer x? (1) 21x is a multiple of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the value of the positive integer x? (1) 21x is a multiple of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards