If 1,500 is increased by 20% and then reduced by $y\%,$ yielding 1,080, what is $y ?$

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

If 1,500 is increased by 20% and then reduced by $y\%,$ yielding 1,080, what is $y ?$

by Vincen » Sat May 30, 2020 2:23 pm

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If 1,500 is increased by 20% and then reduced by $y\%,$ yielding 1,080, what is $y ?$

(A) 20
(B) 30
(C) 40
(D) 50
(E) 60

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT

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Source: Beat The GMAT — Problem Solving | Sat May 30, 2020 2:23 pm

orthodoxparadox: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Sat May 30, 2020 10:48 pm

Re: If 1,500 is increased by 20% and then reduced by $y\%,$ yielding 1,080, what is $y ?$

by orthodoxparadox » Sat May 30, 2020 11:41 pm

When 1500 is increased by 20% it becomes $\frac{120}{100}\ \cdot\ 1500\ =\ 1800$

Now when 1800 is decreased by y% it becomes 1080.

So $$\frac{\left(100\ -\ y\right)}{100}\ \cdot\ 1800\ =\ 1080$$
$\left(100\ -\ y\right)\ \cdot\ 18\ =\ 1080$ $$\left(100\ -\ y\right)=\ \frac{1080}{18}\ =\ 60$$ $$y\ =\ 40$$ C