If y = 2 + 2K and yâ‰ 0yâ‰ 0, then 1/y + 1/y + 1/y + 1/y = ?

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Jan 03, 2019 9:33 pm

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If y = 2 + 2K and y â‰ 0, then 1/y + 1/y + 1/y + 1/y = ?

A. 1/(8+8k)
B. 2/(1+k)
C. 1/(8+k)
D. 4/(8+k)
E. 4/(1+k)

OA B

Source: GMAT Prep

Source: Beat The GMAT — Problem Solving | Thu Jan 03, 2019 9:33 pm

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by Brent@GMATPrepNow » Fri Jan 04, 2019 6:25 am

BTGmoderatorDC wrote:If y = 2 + 2k and y â‰ 0, then 1/y + 1/y + 1/y + 1/y = ?

A. 1/(8+8k)
B. 2/(1+k)
C. 1/(8+k)
D. 4/(8+k)
E. 4/(1+k)

Given: y = 2 + 2k
Rewrite as: y/1 = (2 + 2k)/1
Flip both fractions to get: 1/y = 1/(2 + 2k)

So, 1/y + 1/y + 1/y + 1/y = 1/(2 + 2k) + 1/(2 + 2k) + 1/(2 + 2k) + 1/(2 + 2k)
= 4/(2 + 2k)
= 4/(2)(1 + k)
= 2/(1 + k)

Answer: B

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Brent

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by GMATGuruNY » Fri Jan 04, 2019 6:56 am

BTGmoderatorDC wrote:If y = 2 + 2K and y â‰ 0, then 1/y + 1/y + 1/y + 1/y = ?

A. 1/(8+8k)
B. 2/(1+k)
C. 1/(8+k)
D. 4/(8+k)
E. 4/(1+k)

Let k=0, implying that y = 2 + 2*0 = 2.
Plugging y=2 into 1/y + 1/y + 1/y + 1/y, we get:
1/2 + 1/2 + 1/2 + 1/2 = 2.
The correct answer must yield a value of 2 when k=0.
Only B works:
2/(1+k) = 2/(1+0) = 2.

The correct answer is B.

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by fskilnik@GMATH » Fri Jan 04, 2019 9:40 am

BTGmoderatorDC wrote:If y = 2 + 2K and y â‰ 0, then 1/y + 1/y + 1/y + 1/y = ?

A. 1/(8+8k)
B. 2/(1+k)
C. 1/(8+k)
D. 4/(8+k)
E. 4/(1+k)
Source: GMAT Prep

$$\left. \matrix{
y = 2\left( {k + 1} \right) \hfill \cr
?\,\,:\,\,\,4\left( {{1 \over y}} \right) = {4 \over y}\,\, = f\left( k \right)\,\,\,\,\, \hfill \cr} \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = {4 \over {2\left( {k + 1} \right)}} = {2 \over {k + 1}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by [email protected] » Fri Jan 04, 2019 10:23 am

Hi All,

We're told that Y = 2 + 2K and Y â‰ 0. We're asked for the value of 1/Y + 1/Y + 1/Y + 1/Y. This question can be solved in a number of different ways, including by TESTing VALUES. Since we're adding four fractions with the SAME denominator, we can just use some basic Arithmetic and Algebra rules.

To start, when adding fractions with the same denominator, we add the numerators. For example

1/5 + 1/5 + 1/5 = 3/5

Here, we're adding 1/Y + 1/Y + 1/Y + 1/Y, so we end up with 4/Y. We're told that Y = (2 + 2K). Substituting that value in, we get...

4/(2+2K)

We can then simplify that fraction, giving us...

2/(1+K)

Final Answer: B

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by Scott@TargetTestPrep » Fri Feb 01, 2019 5:40 pm

BTGmoderatorDC wrote:If y = 2 + 2K and y â‰ 0, then 1/y + 1/y + 1/y + 1/y = ?

A. 1/(8+8k)
B. 2/(1+k)
C. 1/(8+k)
D. 4/(8+k)
E. 4/(1+k)

OA B

Source: GMAT Prep

Adding the given fractions we have:

4/y

Since y = 2 + 2k, we have:

4/(2 + 2k) = 4/[2(1 + k)] = 2/(1 + k)

Answer: B

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