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24 Jan 2024, 02:32
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72% (01:55) correct
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Of the 240 toy-import businesses in an association, 80 percent imported toys from Asia and 25 percent imported toys from Europe. How many of these businesses imported toys from Europe but not from Asia?
(1) Of the businesses in the association that imported toys from Asia, 25 percent also imported toys from Europe.
(2) Of the businesses in the association, 15 percent neither imported toys from Asia nor imported toys from Europe.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
2024-01-24_13-31-35.png [ 63.52 KiB | Viewed 7434 times ]
(1) Of the businesses in the association that imported toys from Asia, 25 percent also imported toys from Europe.
(2) Of the businesses in the association, 15 percent neither imported toys from Asia nor imported toys from Europe.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
Attachment:
2024-01-24_13-31-35.png [ 63.52 KiB | Viewed 7434 times ]
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06 Feb 2024, 14:22
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To organize the data, use a MATRIX in which E = Europe, NE = not Europe, A = Asia and NA = not Asia.
Since total Europe = 80% and total Asia = 25%, the matrix at bottom is yielded.
The question stem asks for the value represented by the question mark: Europe but not Asia.
The values in the matrix must add up both horizontally and vertically.
Implication:
All we need is ONE OTHER VALUE to complete the whole matrix.
Statement 1:
The 25% of total Asia that also import from Europe represent the percentage that import from BOTH regions -- the leftmost value in the top row.
With this one other value, we can complete the whole matrix and determine the percentage that import from Europe but not Asia.
SUFFICIENT.
Statement 2:
The center box -- neither Asia nor Europe -- is 15%.
With this one other value, we can complete the whole matrix and determine the percentage that import from Europe but not Asia.
SUFFICIENT.
Since total Europe = 80% and total Asia = 25%, the matrix at bottom is yielded.
The question stem asks for the value represented by the question mark: Europe but not Asia.
The values in the matrix must add up both horizontally and vertically.
Implication:
All we need is ONE OTHER VALUE to complete the whole matrix.
Statement 1:
The 25% of total Asia that also import from Europe represent the percentage that import from BOTH regions -- the leftmost value in the top row.
With this one other value, we can complete the whole matrix and determine the percentage that import from Europe but not Asia.
SUFFICIENT.
Statement 2:
The center box -- neither Asia nor Europe -- is 15%.
With this one other value, we can complete the whole matrix and determine the percentage that import from Europe but not Asia.
SUFFICIENT.
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Screen Shot 2024-02-06 at 3.40.35 PM.png [ 19.36 KiB | Viewed 9089 times ]
26 Aug 2024, 11:53
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Much easier is the Venn diagram approach. A=80%, E=25%.
S1) 25% of A=80% is the intersection between A & E. 80%/4=20%. 25%-20%=5% which is E without A. 240*5/100=12, sufficient
S2) N=15%, 80%+25%-x+15%=100%. We are looking for 25%-X=5%. Same as 1), hence sufficient.
S1) 25% of A=80% is the intersection between A & E. 80%/4=20%. 25%-20%=5% which is E without A. 240*5/100=12, sufficient
S2) N=15%, 80%+25%-x+15%=100%. We are looking for 25%-X=5%. Same as 1), hence sufficient.
