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Bowl S contains only marbles. If 1/4 of the marbles were removed, the

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Bunuel
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Bowl S contains only marbles. If 1/4 of the marbles were removed, the [#permalink] New post   17 Apr 2019, 01:04
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Bowl S contains only marbles. If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl S?

(A) 100
(B) 200
(C) 250
(D) 300
(E) 400
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B
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Prateek1793
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Re: Bowl S contains only marbles. If 1/4 of the marbles were removed, the [#permalink] New post   17 Apr 2019, 01:45
Let's say the number of marbles is X.

If the number of marbles becomes full after adding 100 marbles to 1/2 of the full capacity.

The equation becomes :

X= 100 + 1/2X
Therefore, X=200
B.
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Re: Bowl S contains only marbles. If 1/4 of the marbles were removed, the [#permalink] New post   17 Apr 2019, 02:09
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Bunuel wrote:
Bowl S contains only marbles. If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl S?

(A) 100
(B) 200
(C) 250
(D) 300
(E) 400


Let \(x\) be the number of marbles and let \(C\) be the capacity of the bowl.

We know that \((x-\frac{1}{4}x)=\frac{3}{4}x=\frac{1}{2}C\), so \(C=\frac{6}{4}x=\frac{3}{2}x\).

We also know that \(x+100=C\), so \(x+100=\frac{3}{2}x\).

\(100=\frac{1}{2}x\)

\(x=200\)

Answer: B
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Re: Bowl S contains only marbles. If 1/4 of the marbles were removed, the [#permalink] New post   17 Apr 2019, 02:31
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Bunuel wrote:
Bowl S contains only marbles. If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl S?

(A) 100
(B) 200
(C) 250
(D) 300
(E) 400


total = x
1/4* x removed left with 3x/4=1/2
now 3x/2 =x+100
solve for x= 200
IMO B
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Re: Bowl S contains only marbles. If 1/4 of the marbles were removed, the [#permalink] New post   19 Apr 2019, 10:06
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Bunuel wrote:
Bowl S contains only marbles. If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl S?

(A) 100
(B) 200
(C) 250
(D) 300
(E) 400


We can let n = total marbles in the bowl. Thus, the capacity of the bowl is n + 100 marbles. If 1/4 of the marbles were removed, in other words, if there were 3n/4 marbles in the bowl, the bowl would be filled to 1/2 of its capacity. Thus, the capacity of the bowl is also equal to 2 x 3n/4 = 3n/2. Let’s equate the two expressions we obtained for the capacity of the bowl:

n + 100 = 3n/2

2n + 200 = 3n

n = 200

Answer: B
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Re: Bowl S contains only marbles. If 1/4 of the marbles were removed, the [#permalink] New post   26 Jul 2019, 13:40
Let X be total marbles in the bowl. We have 3/4X (if 1/4X removed we have 1/2X).

If we add 100 marbles to the 3/4X (in the bowl), the bowl would be full. Thus 1/4X = 100 marbles.

Thus, I would conclude that 3/4X equals 300. What am I missing?
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Re: Bowl S contains only marbles. If 1/4 of the marbles were removed, the [#permalink] New post   17 Jan 2024, 05:29
Xin Cho wrote:
Let X be total marbles in the bowl. We have 3/4X (if 1/4X removed we have 1/2X).

If we add 100 marbles to the 3/4X (in the bowl), the bowl would be full. Thus 1/4X = 100 marbles.

Thus, I would conclude that 3/4X equals 300. What am I missing?


You are reading it as just one case with 2 scenarios, but the problem actually states two different cases (the same happened to me too).

The first sentence is

(1)...X - 1/4 X = 1/2 S

Then the second one is
(2)...x + 100 = S

(1) and (2) are independent. Solve for X and X = 200
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Re: Bowl S contains only marbles. If 1/4 of the marbles were removed, the [#permalink] New post   17 Jan 2024, 08:11
Bunuel wrote:
Bowl S contains only marbles. If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl S?

(A) 100
(B) 200
(C) 250
(D) 300
(E) 400

Without any calculations....

The bowl is 50% filled and after adding 100 marbles the Bowl is 100% Full

Thus, 50% represents 100 , as such 100% of the bowl must be 200, Answer must be (B)
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Re: Bowl S contains only marbles. If 1/4 of the marbles were removed, the [#permalink]
17 Jan 2024, 08:11
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