\[ \frac{19^2+19}{20}= \]

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

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$$\frac{19^2+19}{20}=$$ A. 19/10
B. 57/20
C. 19
D. 38
E. 361

The OA is the option C.

What is the fastest way to solve this PD question? May someone clarifies this to me? Thanks.

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Source: Beat The GMAT — Problem Solving | Fri May 11, 2018 7:24 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

192+1920=

by Brent@GMATPrepNow » Fri May 11, 2018 7:52 am

VJesus12 wrote:$$\frac{19^2+19}{20}=$$ A. 19/10
B. 57/20
C. 19
D. 38
E. 361

Notice that we can factor 19 from the numerator.

(19Â² + 19)/20 = (19)(19 + 1)/20
= (19)(20)/20
= 19

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Fri May 11, 2018 8:07 am

VJesus12 wrote:$$\frac{19^2+19}{20}=$$ A. 19/10
B. 57/20
C. 19
D. 38
E. 361

The OA is the option C.

What is the fastest way to solve this PD question? May someone clarifies this to me? Thanks.

Hello Vjesus12.

Here the best way is taking 19 as a common factor as follows: $$\frac{19^2+19}{20}=\frac{19\left(19+1\right)}{20}=\frac{19\cdot20}{20}=19.$$ This way, we get the answer straightforward. Hence, the correct answer is the option C.

I hope this explanation may help you.

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