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13 Jun 2025, 12:12
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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If \(2 < x < 4\) and \(3 < y < 7,\) what is the largest integer value of \(x + y\)?
14 Jun 2025, 23:46
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Given:
To find: The greatest integer value of x + y
Solution:
Before we see the correct solution, let's discuss a Common Mistake.
Often, students find the greatest integer values of x and y separately (3 and 6, respectively) and then add them to get 9 as the answer. But this is WRONG!
See why:
Observe how this 10 is more than the 9 we got earlier. That 9 assumed that x and y also had to be integers.
In reality, having x = 3.5 and y = 6.5 gives us x + y = 10. (There are many other combinations of x and y that can give us 10.)
Key Learning: Never assume numbers to be integers unless explicitly stated. Assumption is a big killer on the GRE.
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
- 2 < x < 4
- 3 < y < 7
To find: The greatest integer value of x + y
Solution:
Before we see the correct solution, let's discuss a Common Mistake.
Often, students find the greatest integer values of x and y separately (3 and 6, respectively) and then add them to get 9 as the answer. But this is WRONG!
See why:
- Adding the two given inequalities, we get 5 < (x + y) < 11.
- Thus, x + y is a real number between 5 and 11, exclusive.
- The greatest integer in this range is 10. And thus, greatest integer value of (x + y) is 10.
Observe how this 10 is more than the 9 we got earlier. That 9 assumed that x and y also had to be integers.
In reality, having x = 3.5 and y = 6.5 gives us x + y = 10. (There are many other combinations of x and y that can give us 10.)
Key Learning: Never assume numbers to be integers unless explicitly stated. Assumption is a big killer on the GRE.
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
19 Jun 2025, 12:39
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OE
If x and y are integers, the largest value is 3 + 6 = 9. However, although x + y is to be an integer, neither x nor y must be. If x = 3.8 and y = 6.2, then x + y = 10.
If x and y are integers, the largest value is 3 + 6 = 9. However, although x + y is to be an integer, neither x nor y must be. If x = 3.8 and y = 6.2, then x + y = 10.
