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

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
If the remainder when positive integer x is divided by 7 is 4, what is [#permalink]

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04 Apr 2018, 22:05
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Difficulty:

35% (medium)

Question Stats:

76% (01:18) correct 24% (01:06) wrong based on 49 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
[Reveal] Spoiler: OA

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Manager
Joined: 05 Feb 2016
Posts: 107
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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04 Apr 2018, 22:19
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
Manager
Joined: 31 May 2017
Posts: 161
Re: If the remainder when positive integer x is divided by 7 is 4, what is [#permalink]

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05 Apr 2018, 20:22
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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If the remainder when positive integer x is divided by 7 is 4, what is [#permalink]

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06 Apr 2018, 23:53
1
KUDOS
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

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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Ujjwal
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If the remainder when positive integer x is divided by 7 is 4, what is   [#permalink] 06 Apr 2018, 23:53
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