If the remainder when positive integer x is divided by 7 is 4, what is

Question

If the remainder when positive integer x is divided by 7 is 4, what is the value of x?

(1) x is less than 50
(2) x is prime

kunalcvrce · Answer

From 1:x<50,7k+4
x=11,18..
insufficient.

From 2:x can be 11,53

combining both x=11

Hence C

akadiyan · Answer

Option 1: The value can be 11 or 1. Not sufficient

Option 2: X is prime. This can be any prime number. Not Sufficient.

Option 1 and 2 - Prime and less than 50 that when divided by 7 gives reminder of 4. Only 11 is the possible option here.

Ans: C

Posted from my mobile device

ujjwal80 · Answer

The answer should be C.

Question says  \frac{x}{7}  = q + 4 and we need to find x.

Statement 1 - x is less than 50.  There could be more than one value of x which will be less than 50 and when divided by 7 gives 4 as remainder. Such as 45, 38, 31, etc. Therefore not sufficient.

Statement 2 - x is prime.  There are more than one values which will satisfy the question stem and statement 2. Wanna know how? see below.
7x1 + 4 = 11 (prime)
7x2 + 4 = 18 (not prime)
7x3 + 4 = 25 (not prime)
.
.
7x7 + 4 = 53 (prime)

BOTH statements combined, there is only one value 11 which is a prime and less than 50 yet gives a remainder of 4 when divided by 7.

Please help me correct if I am wrong.

BrentGMATPrepNow · Answer

Target question :    What is the value of x?

Given : If the remainder when positive integer x is divided by 7 is 4  
When it comes to remainders, we have a nice rule that says: 
  If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.    
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc. 
From the given information, some possible values of x are:  4, 11, 18, 25, 32, 39, 46, 53, 60, 67, . . . etc

Statement 1 : x is less than 50  
The possible values of x are:  4, 11, 18, 25, 32, 39, 46, 53, 60, 67, . . . etc . 
So, statement 1 tells us that  x could equal 4, 11, 18, 25, 32, 39 or 46 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : x is prime 
The possible values of x are:  4, 11, 18, 25, 32, 39, 46, 53, 60, 67, . . . etc . 
From the list, we can already see two prime numbers. 
 x could equal 11 or 53 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
11 is the only possible value of x that satisfies BOTH statements. 
So, the answer to the target question is  x = 11 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=XCxgIR042tE

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If the remainder when positive integer x is divided by 7 is 4, what is

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

If the remainder when positive integer x is divided by 7 is 4, what is

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