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GMAT Official Guide 2019 (1/2 - 1/3) + (1/3-1/4)

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by BTGmoderatorDC » Sun Jul 08, 2018 1:01 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

$$\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)=$$

$$A.\ -\frac{1}{6}$$
B. 0
$$C.\ \frac{1}{3}$$
$$D.\ \frac{1}{2}$$
$$E.\ \frac{2}{3}$$
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by GMATGuruNY » Sun Jul 08, 2018 2:09 am
BTGmoderatorDC wrote:$$\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)=$$

$$A.\ -\frac{1}{6}$$
B. 0
$$C.\ \frac{1}{3}$$
$$D.\ \frac{1}{2}$$
$$E.\ \frac{2}{3}$$
All the values between the first term and the last term CANCEL OUT.
If we subtract the last term from the first term, we get:
$$\ \frac{1}{2}-\frac{1}{6}=\ \frac{3}{6}-\frac{1}{6}=\frac{2}{6} = \frac{1}{3}$$

The correct answer is C.
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by [email protected] » Sun Jul 08, 2018 6:30 pm
Hi All,

When a GMAT question presents what appears to be a 'step heavy' calculation to you, it's important to remember that the Quant section of the GMAT is NOT a 'math test'; it's a 'critical thinking' test that requires lots of little calculations as you work through it. Here, while it may be temping to try to perform each individual calculation, you should note the patterns involved in the work.

Notice that while you 'subtract 1/3' early on, you would then 'ADD 1/3' in the next step, so those two calculations 'cancel out.' The same cancellation occurs with the two 1/4s and so on. Thus, you're ultimately left with 1/2 - 1/6....
1/2 - 1/6 =
3/6 - 1/6 =
2/6 = 1/3

Final Answer: C

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by Scott@TargetTestPrep » Thu Jul 19, 2018 4:25 pm
BTGmoderatorDC wrote:$$\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)=$$

$$A.\ -\frac{1}{6}$$
B. 0
$$C.\ \frac{1}{3}$$
$$D.\ \frac{1}{2}$$
$$E.\ \frac{2}{3}$$
If we remove the parentheses, it is easy to see that all the terms except the first and last are cancelled. So we are left with

1/2 - 1/6 = 3/6 - 1/6 = 2/6 = 1/3

Answer: C

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