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Hoa many thousands of gallons of water does a reservoir have?

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Hoa many thousands of gallons of water does a reservoir have?

by AAPL » Thu Apr 16, 2020 4:26 am

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How many thousands of gallons of water does a reservoir have?

1) If 1/3 of the water in the reservoir were released, then the reservoir would be filled to 1/2 of its capacity.
2) If 60 thousand gallons of water were pumped into the reservoir, it would be filled to capacity.

OA C
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Source: — Data Sufficiency |
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Re: Hoa many thousands of gallons of water does a reservoir have?

by deloitte247 » Sat Apr 18, 2020 1:17 pm

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Let a filled portion of the reservoir = F

Statement 1 => if 1/2 of the water in the reservoir were released then the reservoir would be filled to 1/2 of its capacity.
i.e if 1/3 * F = F/3 volume of water is released, the remainder = 2/3 * F = 2F/3

Given that remainder is equal to half of the total capacity then,
Total * 1/2 = 2F/3
Total = 4F/3 but the value of F is unknown so the total volume is unknown as well
Statement 1 is NOT SUFFICIENT

Statement 2 => if 60 thousand gallons of water were pumped into the reservoir it would be filled to its capacity.
Total capacity = filled + empty portion of reservoir
Let empty portion = E
Total = F + E
E = total - F
Where E = 60,000, => 60,000 = total - F
Value of F is unknown and total cannot estimated. So, statement 2 is NOT SUFFICIENT

Combining both statements together =>
60,000 = total - F => where total = 4F/3
$$60,000=\frac{4F}{3}-\frac{F}{1}=\frac{F}{3}$$
$$F=60,000\cdot3=180,000$$
$$Total=\frac{4\cdot180,000}{3}=240,000\ gallons\ of\ water$$

Both statements together ARE SUFFICIENT
Answer = C
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