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This felt too easy while some 655-level questions feel too hard lol :)

Let the family's total income for May be 100, Mrs. Lee's income is 60, and the rest of the family's income is 40.

In June, she earned 20% more, therefore she earned 72, while the rest of the family's income was same i.e. 40, total family income = 72+40 = 112.

Lee's income as a percent of family income = 72/112*100 = 450/7 = 64.2%. Ans. A
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glagad
Can someone help me with estimations here? I struggled a lot to get from 72/112 to 64%
glagad The answers are spread out enough (4% apart) that we can round a little:

I'd round to 70 / 110 = 7 / 11

1/11 ≈ 9%

7 * 9% = 63% ≈ 64%

(Note that rounding from 72 / 112 to 70 / 110 does not change the result much; it goes from 64.3% to 63.6%. A real-life example would be a basketball player makes 2 free throws, to go from 70/110 to 72/112; the denominator of 112 is big enough that it's not going to change the percentage much.)


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Vordhosbn
Number picking is the way to go here. We can assume family of two.

In May: 60, 40 - assume she made $60 and the other person $40 giving us 60%
In June she made 1.2 more giving us 72 and the other person still made $40. 72/112*100 ~ 64%
Vordhosbn Yes, this is a great method, and I would also pick 100 as the total for May.

Here's how we can organize it into a table and stay organized.


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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%
C is a very common trap here:



In general, don’t forget that if one part of the total changes, the total also changes. A common error is to account for only one of the changes, not both the part and the total.

On this one, if we pick the number 100 for the total in May, we must make sure to put 112 for the new total in June.

Here are some other ones to try, with similar traps:

https://gmatclub.com/forum/of-the-3-600-employees-of-company-x-1-3-are-clerical-if-the-clerical-43660.html#p307338

https://gmatclub.com/forum/of-the-800-employees-of-company-x-70-percent-have-been-with-93778.html#p721534
https://gmatclub.com/forum/when-2-9-of-the-votes-on-a-certain-resolution-have-been-counted-128471.html#p1052792


More broadly, it's essential to build habits for proactive error prevention.

My students find this doc helpful: GMAT Habits for Proactive and Mindful Error Prevention: How to Dodge Common Traps (by Ben@GMATcoach.com)

I suggest making your own copy of this doc and adding to it, based on your own mistakes and insights.
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This is a classic percent problem that trips up a lot of students. The tricky part? You need to recognize that when Mrs. Lee's income increases but everyone else's stays the same, both her earnings AND the total family income change. Let me walk you through how to handle this.

Here's how to think about it:

Step 1: Understand what's happening

In May, Mrs. Lee earned 60% of the family's total income. That means the rest of the family earned 40%. In June, Mrs. Lee got a 20% raise on her May earnings, while everyone else's income stayed exactly the same. You need to find what percent of the new total her June earnings represent.

The key insight here: When Mrs. Lee's income goes up but the rest stays constant, the family's total income increases too. So you can't just add 20% to 60% and call it a day!

Step 2: Use concrete numbers

Let's make this easier by using actual dollar amounts. Since Mrs. Lee earned 60% of the total in May, let's say the family's total income in May was $100.

So in May:
  • Mrs. Lee: $60 (60% of $100)
  • Rest of family: $40 (40% of $100)
  • Total: $100

Step 3: Calculate June earnings

Mrs. Lee earned 20% more in June than in May:
\(20\%\) of \(\$60 = \$12\)

So Mrs. Lee's June earnings: \(\$60 + \$12 = \$72\)

Step 4: Find the new percentage

Now here's where students often slip up. The rest of the family still earned $40, so:

June family income:
  • Mrs. Lee: $72
  • Rest of family: $40
  • New total: $112

Mrs. Lee's percentage in June:
\(\frac{72}{112} = 0.6429 = 64.29\%\)

Approximately 64%

Answer: (A) 64%

Notice how Mrs. Lee's share only went from 60% to about 64%, not to 80%? That's because the denominator (total family income) increased along with her earnings.

Want to master these "changing base" percent problems? The complete solution on Neuron shows you the systematic framework that works every time, plus the common trap variations of this problem type and time-saving techniques. You can check out the step-by-step solution on Neuron by e-GMAT to understand the underlying pattern recognition approach. You can also practice with comprehensive solutions for other official questions here to build consistent accuracy on these problem types.

Hope this helps!
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Family income in May= x


Lee's income 3x/5

Rest of family 2x/5


In June

Lee's income = 120/100 X 3x/5



= 18x/25


Total income will now be 18x/25 + 2x/5


28x/25




Percent of Lee's income in June


18x/25 X 25/28x X 100


approx 64%

Answer A
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