Problem
Four consecutive odd integers have a sum of 48. Find the average of those integers.
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SAT: Multiple-Choice Question #7 |
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Question:
If a and b are positive integers, and if a and b are not prime numbers, which of the following CANNOT be the sum of a and b?
Choices:
The numbers a and b are both positive integers, but not prime numbers. It will probably be fastest if we go through each answer choice and find the one that does not represent a possible sum of a and b.
| (A) |
5 |
= |
1 |
+ |
4 |
. Since 1 and 4 are positive and not prime,
they |
| can be values of |
a |
and |
b |
. Choice (A) isn't the correct answer. |
| (B) |
6 |
= |
1 |
+ |
5 |
= |
2 |
+ |
4 |
= |
3 |
+ |
3 |
. No matter how we add two |
| positive numbers up to equal 6, we have to use a prime number. |
| So 6 can't be the sum of two positive, non-prime integers, |
| and choice (B) is correct. |
| Let's check the other three answer choices, just to be thorough. |
| (C) |
7 |
= |
1 |
+ |
6 |
. |
a |
= |
1 |
and |
b |
= |
6 |
is OK. |
| (D) |
12 |
= |
6 |
+ |
6 |
. |
a |
= |
6 |
and |
b |
= |
6 |
is OK. Also, 4 and 8 work. |
| (E) |
13 |
= |
1 |
+ |
12 |
. |
a |
= |
6 |
and |
b |
= |
6 |
is OK. Also, 4 and 9 work. |
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