If (−x/7) +4 is a positive odd integer, which of the following must be

Question

If (−x/7) +4 is a positive odd integer, which of the following must be true?

A. x is negative. 
B. x is positive. 
C. x is even. 
D. x is odd. 
E. x < 21

IanStewart · Answer

Did they use square brackets in the question? They should not - that notation can have a special meaning (it can indicate a type of rounding function, for example) that they clearly do not intend. The question is just asking about 4 - (x/7). If that's an integer, x must be divisible by 7. But if x were an even multiple of 7, then x/7 will still be even (the '2' in 'x' won't cancel out), and in that case 4 - (x/7) would be even - even = even. So x must be an odd multiple of 7, and the answer is D.

Abhishek009 · Answer

+4 = ODD

Or,    = ODD - 4

Or,    = ODD

Or,    = 7*ODD

Or,    = ODD , Hence x must be Odd (Can be +ve or -ve ), Answer has to be (D)

Fdambro294 · Answer

Given:

-(X) / 7 + 4 = (+)Pos. ODD Integer

Inferences that can be made:

(a)X must be a Multiple of 7 because we need an Integer + Integer = ODD Integer

(b)if X is (+)Positive, then X must be < 28 ---- Otherwise the Magnitude of the (-)Negative Value would surpass the (+)4 and we would have a (-)Negative Value

If X is (-)Negative, then we will have a Positive Value outcome regardless.

(c) Since: ODD +/- EVEN = ODD

-(X/7) + 4 = ODD

-(X/7) = ODD - 4

-(X/7) = ODD - EVEN

-(X/7) = ODD Integer

-(X) = 7 * (ODD Integer)

-(X) = ODD * (ODD Integer)

This means that X MUST = ODD ---

For Example:
if X were to Equal an EVEN Multiple of 7 such as X = -(56)

-(-56/7) + 4 =

+8 + 4 = 12, an EVEN Integer ---- would NOT Satisfy the Conditions

X can = 21, so this is why we can Eliminate -E-

-(21/7) + 4 = -(3) + 4 = +(Positive) 1, which is an ODD Integer

Answer is -D-

X must be ODD

TestPrepUnlimited · Answer

\frac{−x}{7} +4 = +Odd

\frac{−x}{7} = +Odd - 4 = Odd  (at this point it might be negative odd so we don't know the sign).

−x= Odd * 7 = Odd . Thus we can conclude x is odd.

Ans: D

GMATGuruNY · Answer

Case 1:  -\frac{x}{7}+4 =1 
 -\frac{x}{7}=-3 
 -x=-21 
 x=21 
Since x does not have to be negative, even or less than 21, eliminate A, C and E.

Case 2:  -\frac{x}{7}+4 =5 
 -\frac{x}{7}=1 
 -x=7 
 x=-7 
Since x does not have to be positive, eliminate B.

D

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If (−x/7) +4 is a positive odd integer, which of the following must be

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If (−x/7) +4 is a positive odd integer, which of the following must be

Prep Toolkit

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