Source: Revised GRE PDF 1st Ed. Section 6: Math; #12 (p. 87)


Last year Kate spent between 1/4 and 1/3

Last year Kate spent between 1/4 and 1/3 of her gross income on her mortgage payments. If Kate spent $13,470 on her mortgage payments last year, which of the following could have been her gross income last year? Indicate all such gross incomes. $40,200, $43,350, $47,256, $51,996, $53,808

3 Explanations


Zarreen Amin


Can you further explain why it is $13,470*3 (or 4) and not 1/3 or 1/4?

Thank you!

Sep 3, 2017 • Comment

Sam Kinsman, Magoosh Tutor

Sure! Let's say Kate spent between 1/4 of her gross income on her mortgage payments, and we'll call her gross income x.

So we know that 1/4 of x was spent on her mortgage payments. So we can say:

1/4 * x = amount spent on mortgage payments

The problem tells us she spent $13,470 on mortgage payments, so:

1/4 * x = $13,470

Now, we want to solve for x, so we divide both sides by 1/4.

1/4 * x = $13,470
x = $13,470 / (1/4)

This becomes $13,470 * 4 = 53,880.

If you have a hard time seeing how we got $13,470 * 4, think of it this way:

x = $13,470 / (1/4)
x = $13,470 / (0.25) = 53,880

Finally, note that if we did $13,470 * 1/4, we would be calculating 1/4 of her mortgage payments. That's not what we want to do - we want to find 1/4 of her her income, and set that equal to her mortgage payments so we can find her income :)

I hope this helps! :)

Sep 12, 2017 • Reply


Darnell Billups

I got this one wrong when taking the test. I assumed from the wording in the paragraph that they were only looking for values "between" 1/4 and 1/3 of her gross income, so I did not pick $53,808 (4*$13,470) because it is not "between" 4*$13,470 and 3*$13,470. GRE math is not that difficult, but the way they word things is very difficult. I should have focused on the actual question at the end of the second sentence, "which of the following could have been her gross income last year?" Focusing on that statement would have made me select all the right answers because they don't care about "between", they want to know all the values to include both extreme ends of the calculations. I believe this is why the question was set-up this way to catch people who are not reading closely or rushing. So always remember to identify what you are trying to find before solving. It may seem like it will waste time but it will increase the chance of you not falling for the test maker's traps.

Oct 12, 2016 • Comment


Gravatar Chris Lele, Magoosh Tutor

Sep 26, 2012 • Comment

Alyaa Altabbaa


Jun 24, 2015 • Reply

Jonathan , Magoosh Tutor

Hi Alyaa.

Kate spent $13,470 on her mortgage payments last year.
We are total that amount represents between 1/3 and 1/4 of her gross income.

The gross income is higher than the mortgage payments.

If (13,470) spent on mortgage payment is a SMALLER fraction of her income, then that means her INCOME is LARGER.

4 * (13,470) gives us her maximum possible gross income. In this case, (13,470) is 1/4 of the income.

3 * ( 13,470) ) gives us her minimum possible income. In this case, (13,470) is 1/3 of the income.

Hope that helps.

Jun 29, 2015 • Reply

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