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Difficulty: Sub 505 Level,   Arithmetic,                                       
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Re: (2 3/5 - 1 2/3)/(2/3 - 3/5) [#permalink]
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\(\frac{2\frac{3}{5}-1\frac{2}{3}}{\frac{2}{3}-\frac{3}{5}}\)

(A) 16
(B) 14
(C) 3
(D) 1
(E) -1

Problem Solving
Question: 176
Category: Arithmetic Operations on rational numbers
Page: 85
Difficulty: 500


(2 3/5-1 2/3)/(2/3-3/5) = (2+3/5-1-2/3)/(2/3-3/5) = (1-(2/3-3/5))/(2/3-3/5) = 1/(2/3-3/5)-1 = 1/(1/15)-1 = 15 -1 = 14
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Re: (2 3/5 - 1 2/3)/(2/3 - 3/5) [#permalink]
Expert Reply
Quote:

(A) 16
(B) 14
(C) 3
(D) 1
(E) -1


We can simplify the numerator of the fraction by converting the mixed numbers into improper fractions:

[(13/5) - (5/3)]/[(2/3) - (3/5)]

Multiplying the entire expression by 15/15, we have:

(39 - 25)/(10 - 9) = 14/1 = 14

Answer: B
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Re: (2 3/5 - 1 2/3)/(2/3 - 3/5) [#permalink]
1. (2 3/5 - 1 2/3) / 2/3 - 3/5
2. 13/5 - 5/3 / 2/3 - 3/5
3. 14/15 / 1/15
4. 14

Answer is 14, (B)
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Re: (2 3/5 - 1 2/3)/(2/3 - 3/5) [#permalink]
Answer = (B) 14
(2 3/5 - 1 2/3) / 2/3 - 3/5
13/5 - 5/3 / 2/3 - 3/5
-14/15 / -1/15
14
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Re: (2 3/5 - 1 2/3)/(2/3 - 3/5) [#permalink]
Expert Reply
Bunuel wrote:

\(\frac{2\frac{3}{5}-1\frac{2}{3}}{\frac{2}{3}-\frac{3}{5}}\)

(A) 16
(B) 14
(C) 3
(D) 1
(E) -1


Fractions are no fun. Let's convert to decimals and ballpark our way to the right answer without finding even a single common denominator!!
FWIW, this is PS question 211 out of 212 in the 2022 OG Quant, so GMAC seems to think it's among the hardest questions in the book. LOL.

\(\frac{(2.6-1.667)}{(0.667-0.6)}\)

I'll go ahead and ballpark the numerator to be 1. Yeah, it's a little less than 1, but I'll address that later if it ends up mattering.

Denominator is 0.067.

So we've got \(\frac{1}{0.067}\). That's 15 (1/0.033333 is 30, right?)

Okay, so 15. C, D, and E are definitely wrong. But yikes, A and B are both really close!

Do we want something larger than 15 or something smaller? Remember when I ballparked the numerator to be a little bigger than it really is. So we need to go a little smaller than 15. Answer choice A is wrong.

Answer choice B.

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Re: (2 3/5 - 1 2/3)/(2/3 - 3/5) [#permalink]
Recognize that the mixed fractions in the numerator are a sum of a quotient and
a fraction.

The fractions in the numerator are the same as those in the numerator but the operations are switched, so that piece is -1.

This leaves the operation on the quotients remaining, 2-1 = 1/((2/3)-(3/5))

Solving this as mentioned in prior answers is 14.

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Re: (2 3/5 - 1 2/3)/(2/3 - 3/5) [#permalink]
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Re: (2 3/5 - 1 2/3)/(2/3 - 3/5) [#permalink]
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