If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an

Question

Competition Mode Question

If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
(2) z^3 is even.

firas92 · Answer

(1) (z + 7)/3 = 2m + 1, where m is an integer.

z+7=3(2m+1)

(2m+1) is always odd and so 3(2m+1) is odd

z+7=odd
z=odd-7=even

1 is sufficient

(2) z^3 is even.

Since we are given that z is an integer, if z^3 is even then z is even since raising an integer to an integer power does not change the odd-even nature

2 is sufficient

Answer is D

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Leadership · Answer

If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
 Re-writing: Z + 7 = 3 (2m + 1) ... Z = 3 (2m + 1) - 7
We know 2m will always be EVEN irrespective of what 'm' is. 
2m + 1 = Will be always odd (even + odd = odd)
3 (2m + 1) = Will be always odd (odd * odd = odd)
3 (2m + 1) - 7 = will be always even (odd - odd = even)

Sufficient

A D /  B C E

(2) z^3 is even.
 From the number properties we know that even^3 = even and odd^3 = odd.
Hence, Z will be always Even. Sufficient

'D' is the winner

Archit3110 · Answer

#1
(z + 7)/3 = 2m + 1, where m is an integer.
LHS ; 2m+1 will be odd ; so now to get LHS as odd value of z has to be even ; sufficient
#2
z^3 is even
z has to even integer; sufficient
IMO D

If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
(2) z^3 is even.

GMATinsight · Answer

Question : Is integer z even?

Statement 1 : (z + 7)/3 = 2m + 1 
since, m is an integer, (z + 7)/3 = 2m + 1 = odd

i.e. (z + 7) =3* Odd
i.e. z = 3* odd - 7 = Odd - Odd = Even

SUFFICIENT

Statement 2 : z^3 is even 
since, z is an integer therefore, z^3 also will be an integer
and since z^3 is even so z also must be even

SUFFICIENT

Answer: Option D

P.S. The question would have been far more trickier if the question had not mentioned that z is an Integer because 2nd statement then would have been Insufficient

freedom128 · Answer

(1) (z+7)/3= odd --> z+7= 3*odd= odd --> z is even
SUFFICIENT
 
(2) z^3 is even.
If z^3 is even, then z is even
SUFFICIENT

FINAL ANSWER IS (D)

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unraveled · Answer

If z is an integer, is z even?

(1)  \frac{(z + 7)}{3} = 2m + 1 , where m is an integer.
2m + 1 = odd since m is an integer.
 \frac{(z + 7)}{3} = 2m + 1  =  \frac{e + o}{o} = o

z is even.

SUFFICIENT.

(2)  z^3  is even.
 even^3  = even

z is even.

SUFFICIENT.

Answer D.

lacktutor · Answer

If z is an integer, is z even?

(Statement1):  \frac{(z + 7)}{3}= 2m + 1 , where m is an integer.
—> z+7 = 6m+ 3 
z= 6m —4 = 2( 3m—2) 
Z—even 
Sufficient

(Statement2):  z^{3}  is even. 
Since  z^{3}  is even, z must be even 
(Even if z is equal to zero) 
Sufficient

The answer is D

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exc4libur · Answer

z is integer

(1) sufic 
z+7/3=2m+1
z+7/odd=even+odd=odd
z+7=odd*odd=odd
z+odd=odd
z=odd-odd=even

(2) sufic 
z^3=even then z=even, because if z=odd then an odd^3=odd

Ans (D)

ostrick5465 · Answer

If z is an integer, is z even?

(1)  \frac{z + 7}{3} = 2m + 1 , where m is an integer.
=> z+7 = 6m+3
=> z = 6m - 4 
=> z is even
=> Suff

(2)  z^3  is even.
For example z^3 = 8 => z=2 => z is even
but  z^3 = 6 => z = \sqrt 6  => z is not an integer.
=> Not suff

=>  Choice A

Jawad001 · Answer

If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
(2) Z^3 is even.

From statement (1), (z + 7)/3 = 2m + 1, where m is an integer.
Or, (z + 7) = 3(2m + 1)
Or, z = 3(2m + 1) – 7
Or, z = 3( 2 *even/Odd + 1) -7
Or, z = 3(even + 1) – 7
Or, z = Odd *Odd -7
Or z = Odd –odd = Even, Sufficient.

From statement (2),
(2) Z^3 is even.
Z is even. Sufficient.

Answer: D

vthatha · Answer

(1) (z + 7)/3 = 2m + 1, where m is an integer.

z = 2(3m) + 3 - 7
z = 2(3m) -4
z = even - even 
z is even --> sufficient

(2) z^3 is even.
z^3 = Z * Z * Z

if z is odd, then Z^3 --> (( Z * Z ) * Z) is ((odd) * odd) = odd
if z is even, then Z^3 --> (( Z * Z ) * Z) is ((even) * even) = even --> Sufficient

If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an

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GMAT Data Sufficiency (DS) Questions

If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an

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