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TheNightKing
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If x = 6m^2 + 4n^2, what is the greatest even number that must be a fa 13 Jul 2019, 18:14
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

18% (01:43) correct 82% (01:42) wrong based on 68 sessions

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If x = 6m^2 + 4n^2, what is the greatest even number that must be a factor of x?

(1) m and n are even
(2) GCF(m,n)=2


Source: McGraw GMAT 11th Edition
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D
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Mo2men
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If x = 6m^2 + 4n^2, what is the greatest even number that must be a fa Updated on: 13 Jul 2019, 19:27
Originally posted by Mo2men on 13 Jul 2019, 18:53.
Last edited by Mo2men on 13 Jul 2019, 19:27, edited 2 times in total.
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RajeshKanjan
DS Question:

If x=6m^2+4n^2, what is the greatest even number that must be a factor of x?
1. m and n are even
2. GCF(m,n)=2

Source: McGraw GMAT 11th Edition
Show more

Dear GMATPrepNow Brent

Can you please shed light on this question. I do not know how answer would be D.

In Statement 1:

Let m=n=2..........x=24+16=40......then 40 is the greatest even number.

Let m=4 & n=2..........x=96+16=112......then 112 is the greatest even number.

It must insufficient.

In statement 2:

I can repeat same examples above and get same answers ...So insufficient

Answer must be E

What is the problem here? Can you help please?

Thanks in advance
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If x = 6m^2 + 4n^2, what is the greatest even number that must be a fa 13 Jul 2019, 19:13
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Since,GCF(m,n)=2
m=2k
n=2h where h and k are coprime.
X=6(2k)^2+4(2h)^2
=24k^2+16h^2
=8(3k^2+2h^2)
Since k and h will be odd other term will always be odd.
So 8 will be the greatest even factor of x

Ans. Both statements are required

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m1033512
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If x = 6m^2 + 4n^2, what is the greatest even number that must be a fa 13 Jul 2019, 19:44
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It brings "must be " phrase here .

so from statement 1 ,

let m = 2k
n = 2k

then we can take minimum 8 common

now , if you replace m and n with any even number , 8 will.always be a factor of x ( if you factorize x , it will always have atleast one 8 as factor )


sufficient


statement 2


himanshu just solved above ,

it is 8 again



IMO D

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BrentGMATPrepNow
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If x = 6m^2 + 4n^2, what is the greatest even number that must be a fa 14 Jul 2019, 06:32
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Mo2men
RajeshKanjan
DS Question:

If x=6m^2+4n^2, what is the greatest even number that must be a factor of x?
1. m and n are even
2. GCF(m,n)=2

Source: McGraw GMAT 11th Edition

Dear GMATPrepNow Brent

Can you please shed light on this question. I do not know how answer would be D.

In Statement 1:

Let m=n=2..........x=24+16=40......then 40 is the greatest even number.

Let m=4 & n=2..........x=96+16=112......then 112 is the greatest even number.

It must insufficient.

In statement 2:

I can repeat same examples above and get same answers ...So insufficient

Answer must be E

What is the problem here? Can you help please?

Thanks in advance
Show more

The target question asks for the greatest even number that must be a FACTOR of x.
So, x COULD equal 40, or x COULD equal 112, or x COULD equal 60, or . . .
Notice that 8 is a factor of all possible values of x.
In fact, 8 is the greatest even number that must be a FACTOR of x

Cheers,
Brent
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If x = 6m^2 + 4n^2, what is the greatest even number that must be a fa 15 Jun 2023, 05:20
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Mo2men
RajeshKanjan
DS Question:

If x=6m^2+4n^2, what is the greatest even number that must be a factor of x?
1. m and n are even
2. GCF(m,n)=2

Source: McGraw GMAT 11th Edition

Dear GMATPrepNow Brent

Can you please shed light on this question. I do not know how answer would be D.

In Statement 1:

Let m=n=2..........x=24+16=40......then 40 is the greatest even number.

Let m=4 & n=2..........x=96+16=112......then 112 is the greatest even number.

It must insufficient.

In statement 2:

I can repeat same examples above and get same answers ...So insufficient

Answer must be E

What is the problem here? Can you help please?

Thanks in advance
Show more

I too have the same issue
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