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07 Jun 2023, 08:15
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (02:31) correct
41%
(01:49)
wrong
based on 76
sessions
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2a3 is a 3-digit positive integer. If 2a3 + 366 = 6b9, what is the value of a + b ?
(1) 2a3 is divisible by 3.
(2) 6b9 is divisible by 9.
(1) 2a3 is divisible by 3.
(2) 6b9 is divisible by 9.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
08 Jun 2023, 09:16
Kudos
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Bunuel
We can use the place value concept to make the original equation more accessible:
2a3 + 366 = 6b9
(203 + 10a) + 366 = (609 + 10b)
10a = 10b + 40
a = b + 4
We need to answer the question:
a + b = ?
Statement One Alone:
=> 2a3 is divisible by 3.
An integer is divisible by 3 if and only if the sum of its digits is divisible by 3, so
2 + a + 3 is div by 3, or a + 5 is div by 3
If a is 1, then b is -3 (= 1 – 4), which is not a valid case.
If a is 4, then b is 0 (= 4 – 4) and a + b = 4.
If a is 7, then b is 3 (= 7 – 4) and a + b = 10.
Statement one is not sufficient. Eliminate answer choices A and D.
Statement Two Alone:
=> 6b9 is divisible by 9.
An integer is divisible by 9 if and only if the sum of its digits is divisible by 9, so
6 + b + 9 is div by 9, or b + 15 is div by 9
In the only valid case, b is 3, a is 7 (= 3 + 4), and a + b is 10.
Statement two is sufficient.
Answer: B
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