If a and b are integers, is a + b + 3 an odd integer?
(1) ab is an odd integer.
(2) a − b is an even integer.
OA D
Source: Official Guide
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If a and b are integers, is a + b + 3 an odd integer? (1)
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BTGmoderatorDC
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Target question: Is a + b + 3 an odd integer?BTGmoderatorDC wrote:If a and b are integers, is a + b + 3 an odd integer?
(1) ab is an odd integer.
(2) a − b is an even integer.
OA D
Source: Official Guide
Given: a and b are integers
Statement 1: ab is an odd integer.
Some useful rules:
1. ODD - ODD = EVEN
2. ODD - EVEN = ODD
3. EVEN - ODD = ODD
4. EVEN - EVEN = EVEN
5. (ODD)(ODD) = ODD
6. (ODD)(EVEN) = EVEN
7. (EVEN)(EVEN) = EVEN
Since ab is odd, we can be certain that a and b are both ODD
If a and b are both ODD, then a + b + 3 = (ODD) + (ODD) + 3 = EVEN + 3 = ODD. In other words, a + b + 3 is an odd integer
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: a − b is an even integer
If a - b = even, then EITHER a is odd and b is odd OR a is even and b is even
In ether case, a + b = EVEN
a + b + 3 = EVEN + 3 = ODD.
In other words, a + b + 3 is an odd integer
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
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BTGmoderatorDC wrote:If a and b are integers, is a + b + 3 an odd integer?
(1) ab is an odd integer.
(2) a − b is an even integer.
a+b+3 = ODD only if a and b are both odd or both even.
Question stem, rephrased:
Are a and b both odd or both even?
Statement 1:
ab = ODD implies that a and b are both odd.
Thus, the answer to the question stem is YES.
SUFFICIENT.
Statement 2:
a-b = EVEN implies that a and b are either both odd or both even.
Thus, the answer to the question stem is YES.
SUFFICIENT.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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