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GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
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04 Jan 2017, 05:12
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What is the median of the 5 consecutive integers?
1) The average (arithmetic mean) of the 5 consecutive numbers is 5
2) The average (arithmetic mean) of the 5 consecutive numbers is an odd number
==> In the original condition, there is 1 variable (and, n+1, n+2, n+3, n+4), and in order to match the number of variables to the number of equations, there must be 1 equation as well. Therefore, D is most likely to be the answer.
For con 1), in case of consecutive numbers, you get median=mean, and thus median=5 and it is sufficient.
For con 2), median=1,3,5,.. and hence it is not unique and not sufficient. Therefore, it is a question where A becomes the answer, but you must be aware of CMT 3. Con 2) and con 1) must be independent from each other, and you can’t assume that they are the same after solving con 1).
The answer is A.
Answer: A
1) The average (arithmetic mean) of the 5 consecutive numbers is 5
2) The average (arithmetic mean) of the 5 consecutive numbers is an odd number
==> In the original condition, there is 1 variable (and, n+1, n+2, n+3, n+4), and in order to match the number of variables to the number of equations, there must be 1 equation as well. Therefore, D is most likely to be the answer.
For con 1), in case of consecutive numbers, you get median=mean, and thus median=5 and it is sufficient.
For con 2), median=1,3,5,.. and hence it is not unique and not sufficient. Therefore, it is a question where A becomes the answer, but you must be aware of CMT 3. Con 2) and con 1) must be independent from each other, and you can’t assume that they are the same after solving con 1).
The answer is A.
Answer: A
05 Jan 2017, 05:39
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If x and y are positive integers, are they consecutive?
1) x+y=3
2) x-y=1
==> In the original condition, there are 2 variables (x, y), and in order to match the number of variables to the number of equations, there must be 2 equations as well. Therefore, C is most likely to be the answer. By solving con 1) and con 2),
For con 2), it is always yes, hence it is sufficient.
For con 1), only (x,y)=(1,2), (2,1) satisfies, hence it is yes.
This question is also related to CMT 4(B). The answer is D.
Answer: D
1) x+y=3
2) x-y=1
==> In the original condition, there are 2 variables (x, y), and in order to match the number of variables to the number of equations, there must be 2 equations as well. Therefore, C is most likely to be the answer. By solving con 1) and con 2),
For con 2), it is always yes, hence it is sufficient.
For con 1), only (x,y)=(1,2), (2,1) satisfies, hence it is yes.
This question is also related to CMT 4(B). The answer is D.
Answer: D
06 Jan 2017, 02:39
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If r and s are positive integers, is the least common multiple of r and s equal to the product of r and s?
1) r and s are consecutive odd numbers
2) r=s+2
==> In the original condition, there are 2 variables (r, s), and therefore C is most likely to be the answer. By solving con 1) and con 2), it is yes, hence sufficient. Therefore, C is the answer. However, since it is an integer question, one of the key questions, if you apply CMT 4(A) on con 1), you get yes and hence it is sufficient.
Therefore, the answer is A.
Answer: A
1) r and s are consecutive odd numbers
2) r=s+2
==> In the original condition, there are 2 variables (r, s), and therefore C is most likely to be the answer. By solving con 1) and con 2), it is yes, hence sufficient. Therefore, C is the answer. However, since it is an integer question, one of the key questions, if you apply CMT 4(A) on con 1), you get yes and hence it is sufficient.
Therefore, the answer is A.
Answer: A
