Bunuel wrote:
What is 35% of 4/13 of 520?
(A) 56
(B) 84
(C) 160
(D) 182
(E) 250
Kudos for a correct solution.
MANHATTAN GMAT OFFICIAL SOLUTION:This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 520, or 1/9 of 520. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
Even the last step in this problem can be approximated. Pick a convenient number nearby, such as 540, which is 9 × 60. Thus, 1/9 of 520 is about 60.
The correct answer must be A.Actually, since 520 is less than 540, 1/9 of 520 must be slightly less than 60. Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
In a problem such as this one, making a logical error or omitting a step in the computation is the trap.
For example, if you computed 4/13 of 520 but didn't take 35% of the result, you would get 160 and select answer choice C incorrectly. If instead you computed 35% of 520 but didn't take 4/13 of the result, you would get 182 and select answer choice D—again, incorrectly. On every problem, follow good process to avoid needless mistakes.
The wording of the question can sometimes provide a strong clue that estimation should be used. Look for phrases such as these:
* “…the number is approximately equal to:”
* “…this result is closest to:”
* “Which of the following is most nearly equal to…?”
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