Right now, a barrel of water is exactly 40% full of water. What is th

(1) If the water in the barrel right now were increased by 25%, then the barrel would be exactly half full.

\(\frac{5}{4} * \frac{2}{5}* X = \frac{1}{2}*X\)

cannot determine X .

NS

(2) If a volume of water equal to half of what is in the barrel right now were added to the barrel, the empty space left in the barrel then would equal 75% of the volume of the water now.

new volume of barrel \((\frac{3}{5}X)\)

empty space=\(\frac{2}{5}X = \frac{3}{4} *\frac{3}{5}*X\)

cannot determine X .

NS

Answer E

VERITAS PREP OFFICIAL SOLUTION:

In this problem, both statements are tautological. That is to say, each one, in a less-than-obvious way, rephrases the information in the prompt. In a way, we simply have the same information, the information already given in the prompt, recycled in three different ways. No new information is added by either statement.

From the prompt, we know that the barrel is 40% full of water right now.

Well, suppose a barrel is 40%, and we increase the water by 25%, or 1/4. That would mean adding a quarter of 40%, or 10% of the barrel to what is already in the barrel. This would increase the barrel to 50%, which is exactly what statement #1 tells us.

Go back to the 40% full barrel: the empty space is 60%. Half of that is 30%. Suppose we add 30% more: then the water would be 70% of the barrel, and the new empty space would be 30%. The new empty space, 30%, is 3/4, or 75%, of the old amount of water, 40%. This is exactly what statement #2 tells us.

Of course, the prompt by itself is never sufficient, and if neither statement adds any new information, then even altogether, we can’t deduce anything.

A totally different way to say this is: the prompt is asking for an actual quantity, the real volume of the barrel, but the prompt & statements give us nothing but ratio information (including percents & fractions). We need a real measurement to get a real measurement, and we never get one in this problem.

Nothing is sufficient.

Answer = (E)

Bunuel niks18 gmatbusters

As per Magoosh OE we added 0.1X and 0.4X and as per Lucky2783 we performed multiplication of fractions.
Can you explain the difference in approach?

hi adkikani

40%=2/5 when this is increased by 25% i.e. 1/4, the resulting fraction will be 1+1/4=5/4

both are same thing. if you are comfortable with fractions, then use that else use decimals.

Hi

If x is increased by 25%, we can do it in number of ways:

1) x +25% of x = x+0.25x = 1.25x

2) x + x/4 = 5x/4 = we simply multiply by 5/4 to the original term.



In fact this method is quite handy

Increase by 10% = multiply by 11/10

decrease by 10% = multiply by 9/10

Increase by 20% = multiply by 6/5

decrease by 20% = multiply by 4/10

Increase by 12.5% = multiply by 9/8



Read the Chapter Fractions/Decimals/percentage . You will understand it better.


As per Magoosh OE we added 0.1X and 0.4X and as per Lucky2783 we performed multiplication of fractions.
Can you explain the difference in approach?[/quote]

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