Mary’s annual income is $15,000 and John’s annual income is

Question

Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 55% of Mary and John’s combined income?

(A) $3,000
(B) $4,000
(C) $7,000
(D) $11,000
(E) $25,000

Source: Gmat Hacks 1800

BrushMyQuant · Accepted Answer

Given that Mary’s annual income is $15,000 and John’s annual income is $18,000. And we need to find By how much must Mary’s annual income increase so that it constitutes 55% of Mary and John’s combined income?

Let Mary's income increase by x, then the equation will be :

Mary's Annual Income( 15,000 ) + Increase in Mary's Annual Income( x ) = ( 55%)  * (Mary's Annual Income( 15,000 ) + Increase( x ) + John's Annual Income( 18,000 ))
=> 15,000 + x= (55/100)* (15,000 + x + 18000 )
=> 15,000 + x = (11/20) * (33,000 + x)
=> 20*(15,000 + x) = 11 * (33,000 + x)
=> 300,000 + 20x = 363,000 + 11x
=> 20x - 11x = 363,000 - 300,000
=> 9x = 63,000
=> x =  \frac{63,000}{9} 
=> x = 7,000

So,  Answer will be C 
Hope it helps!

Bunuel · Answer

Plug in method works for this question perfectly.

Try the middle number: if Mary's annual income increase by $7,000, her income will be $22,000 and combined income will be 22,000 + 18,000 = $40,000. 55% of $40,000 is exactly $22,000.

Answer: C.

Hope it helps.

sshivanis04 · Answer

Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 55% of Mary and John’s combined income?

Let X be the combined income.
Since only Mary's income is increasing then John's income 18000 must constitute 45% of the total income , thus
18000 = 45% of X
X = 18000*100/45 
X= 40000

Thus increase in Mary's income is 40000 - (18000+15000) = 7000.

jlgdr · Answer

Should they mention to constitute 55% of Mary and John combined income after the increase? Cause for me it is not 100% clear.
What do you guys think about the language?

Cheers
J

PareshGmat · Answer

Mary................. John ............... Total
15000 ................ 18000 ................... 33000

Lets say Mary's income increases by x

15000+x .............. 18000 .................... 33000+x

Post increment, Mary's income should constitute 55% of total combined; this also means that John's income should constitute 45%

This step helps variable "x" to be in only one side of the equation

\frac{45}{100} (33000+x) = 18000

x = 7000

Answer = C

SVaidyaraman · Answer

Let Mary's income increase by x.

(15000+x) /(33,000+x) = 55/100
x=7000

Lucky2783 · Answer

Current ratio is 
 \frac{15000}{33000} = \frac{15}{33}  what should be added to denominator and numerator to make it  \frac{55}{100}  or  \frac{11}{20}  or  \frac{22}{40}  .

Adding 7 will make  \frac{15+7}{33+7}  =  \frac{22}{40}

Answer 7000.

C

chesstitans · Answer

the trick is to use 11/20 rather than 0.55, there is no secret in this question. It should not be hard at all.

hellosanthosh2k2 · Answer

Using weighted average method:

New Mary's income <--------45----------|---------55----->18K(John's)

Mary's new/Johns = 55/45
Mary's new = (11/9) * 18 = 22K
so increment must , 22000 - 15000 = 7000

FJ24 · Answer

How did you guys know that the language was referring to combined income after the increase? I originally referred to the combined income as 33, which then leads to 55% as $18,150. Thus leading me to believe, Mary's increase would be $3150 (which is obviously not right in this case). I want to avoid incorrect language interpretation in the GMAT for future questions.

AkshdeepS · Answer

generis

I also have the same question in mind. I calculated 55% of $ 33000, and that comes out to be 18150.

KarishmaB · Answer

It is the logical result of increasing Mary's income.

Mary's income should constitute 55% of Mary and John’s combined income. If Mary's income is higher, Mary and John's combined income automatically is higher. You cannot say that their combined income stayed the same even though Mary's income increased.

Kinshook · Answer

Given:  Mary’s annual income is $15,000 and John’s annual income is $18,000.

Asked: By how much must Mary’s annual income increase so that it constitutes 55% of Mary and John’s combined income?

Let the increase in Mary's annual income be $x

Mary's annual income = $15000 + $x
John's annual income = $18000
Combined income = $33000 + $x

(15000+x)/(33000+x) = 55% = .55
(15000+x)/18000 = .55/.45 = 11/9
15000 + x = 22000
x = $7000

IMO C

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Mary’s annual income is $15,000 and John’s annual income is

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