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Math Expert V
Joined: 02 Sep 2009
Posts: 53865
If the remainder when positive integer x is divided by 7 is 4, what is  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 69% (01:25) correct 31% (01:23) wrong based on 134 sessions

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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

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Manager  G
Joined: 05 Feb 2016
Posts: 156
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: If the remainder when positive integer x is divided by 7 is 4, what is  [#permalink]

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Bunuel wrote:
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

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

From 2:x can be 11,53

combining both x=11

Hence C
Senior Manager  G
Joined: 31 May 2017
Posts: 316
Re: If the remainder when positive integer x is divided by 7 is 4, what is  [#permalink]

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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

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Manager  B
Joined: 27 Jul 2017
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If the remainder when positive integer x is divided by 7 is 4, what is  [#permalink]

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1
Bunuel wrote:
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

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.

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Re: If the remainder when positive integer x is divided by 7 is 4, what is  [#permalink]

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Top Contributor
Bunuel wrote:
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

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

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_________________ Re: If the remainder when positive integer x is divided by 7 is 4, what is   [#permalink] 20 Dec 2018, 06:56
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# If the remainder when positive integer x is divided by 7 is 4, what is

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