In May Mrs Lee's earnings were 60 percent of the Lee family'

In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?

(A) 64%
(B) 68%
(C) 72%
(D) 76%
(E) 80%

Let total income of the family be 100$. In May Mrs Lee's earnings were 60 percent = 60$. Rest of the family's earnings = 40$.

In June family's earnings did not change = 40$, Mrs Lee's earnings = 60$*1.2 = 72$. Total = 40 + 72 = 112$. Mrs Lees share = \(\frac{72}{112}\approx{64%}\).

Answer: A.
_________________

I think Gmat shouldn't trick us with wording like "total". Quant is already tough and making such questions it just throw me off sometimes.

Though I understand above explanation , considering rest of Family income is fixed it is 64%

What is wrong with this method?
Equation1 ...............ML(May Lee) = 60/100 F (Family);
Equation 2 ................ JL(June Lee) = 120/100 ML
Substitute Equation1 in equation 2
JL = 120/100*(60/100*F)
JL = 72/100*F ... So JL is 72% of Family income

As lee is a family member so his portion is included in the total income.
_________________

In May

Lee's income = (60/100)T where T is the family total income in may.

Rest of the family's income = (40/100)T

In June

Lee's income in june = (120/100) (60/100) T = (72/100)T
Rest of the family's income is same as their may's income = (40/100)T


so lee's income as a percentage of total family's income in June = 72/112 = 64%

Answer is A.

Ans is A
let total income is x so Mrs Lee income is 0.6x so rest of family income is 0.4x
mow her salary inc by 20% so it now becomes 0.72x but the remaining income remains 0.4x so now the total family income is 1.12x so 0.72x/1.12x

I hate it when GMAT tricks us with questions.

I chose C

Hi all. This question was one I got wrong on a practice test (which unfortunately doesn't give or explain the correct solution). I think I must just be looking at it the wrong way though it doesn't seem like a difficult question at all. Another point of view and explanation would be appreciated. Thanks!

In May Mrs. Lee's earnings were 60% of the Lee family's total income. (I wrote down 0.6x) In June Mrs. Lee earned 20% more than in May. ((1.2)(0.6x) maybe this is where I went wrong?) If the rest of the family's income was the same in both months, then what percent of the Lee family's total income did Mrs. Lee earn in June?

64% - 68% - 72% - 76% - 80%

My answer was 72% because (1.2(0.6x)) = .72x But I'm guessing now that I wrote it out wrong?

The only thing you did wrong is that while calculating Lee's new share you considered the same base i.e. x

Lee families income (May) = x
Lee's share in that (60%) = 0.6x
Lees' income in june = 0.72x
Lee families income (June) = 1.12x
Lee's new share = 64.28%

Or solve it with simple values

Lee families income (May) = 100
Lee's share in that (60%) = 60
Lees' income in june = 72
Lee families income (June) = 112
Lee's new share = 64.28%

This question is testing how carefully we can read the problem. Like many of you, I failed to do so and chose C until I carefully reread the problem and saw my error.

Sample numbers are good here.

In May
Family Income = 100
Lee = 60
Rest = 40

In June
Lee = 60*1.2=72
Rest (since it is unchanged) = 40
Family = 112

72/112=approx 64%

A

We can let 100 = the Lee family’s total income in May. Thus, Mrs. Lee made 60, and the rest of the family made 40. Since Mrs. Lee made 20% more in June than in May, she made 60 x 1.2 = 72 in June. Since the rest of the family still made 40, Mrs. Lee’s earnings were

72/(72 + 40) = 72/112 ≈ 0.64 = 64% of the family’s total income.

Answer: A
_________________

Let the family earnings in May = $100

Mrs. Lee earned 60% of 100 = $60

The rest of the family earned 100 - 60 = $40


In June, Mrs. Lee earned 20% more = \(60 \space * \space \frac{120}{100} = $72\)

The rest of the family had no change in their earnings, and hence their earning was still $40.

Therefore, in June, the total Family's earnings was $112 of which Mrs. Lee earned $72


\(\frac{Percentage}{100} \space * \space Total = Portion\)

\(\frac{Percentage}{100} \space * \space 112 = 72\)

% = \(\frac{72}{112} \space * \space100 = 64.28 \space \approx 64\)%


Option A

Arun Kumar

If we assume Lee's family income to be 100, then in May Lee earns 60, and the rest of the family earns 40.

In June, Lee earns 60 * \(\frac{120}{100}\) = 72 and rest of the family earns 40.

=> Mrs. Lee's earnings (72) were approximately what percent of the Lee family's total income ( 72 + 40 = 112)

=> 72 is what percent of 112

=> \(\frac{{72 * 100} }{ 112}\) ≈ 64

Answer A

Answer

let family salary be $100
so Mrs Lee salary ; $60
later she earns 20% more ; her salary becomes $72
and total family salary 112 $ due to Mrs Lee salary increae
% of Mrs Lee salary ; 72/112 ; ~ 64%
option A

Total Family Income = 100 ; Lee's Salary in May = 60

Lee's Salary in June = 72 ; Total Family Income = 112

So, in June, Mrs Lee's earnings were 72/112*100 = 64% (appx) , ANswer must be (A)
_________________

I always end up making some silly mistakes on percent problems. Any ideas on how to improve that. I chose C here which is apparently wrong.

In May, Family's income = 100
so, Lee's income = 60 (60%)
The Rest of the members' income of the family 40.

In June Lee's income 60*1.20= 72
Family's income (without Lee) = 40 (is same; as given in the question)
Now, Total income of the family in Jue 72+40 = 112 (as Lee is family member)

New Percentage = (72/112)*100 = 64.
Ans. A
_________________

In May:

If the Total family (of which Mrs. Lee is a part of) earned $100:

$60 was earned by Mrs Lee

$40 was earned by other family members


In June:

Mrs Lee earned 20% more———> $72

The rest of the family earned the same amount ———> $40
_________________________
Total Family Income = $112


In June, Mrs Lee’s earnings were what percent of the Total Family Income?

($72 / $112) * 100% =

(9 / 14) * 100% = (.64) * 100% =

64%

-A-

Posted from my mobile device

Intially the division is 60 , 40

Later on it becomes 72,40

When expressed in % becomes 64.28

THerefore IMO A