[GMAT math practice question]
If x and y are integers greater than 1 and x>y, what is the value of x?
1) x+y=10
2) xy=21
If x and y are integers greater than 1 and x>y, what is t
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- Max@Math Revolution
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Target question: What is the value of x?Max@Math Revolution wrote:[GMAT math practice question]
If x and y are integers greater than 1 and x>y, what is the value of x?
1) x+y=10
2) xy=21
Given: x and y are integers greater than 1 and x > y
Statement 1: x+y=10
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 9 and y = 1. In this case, the answer to the target question is x = 9
Case b: x = 8 and y = 2. In this case, the answer to the target question is x = 8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: xy=21
Since x and y are INTEGERS greater than 1 AND x > y, we can see that it MUST be the case that x = 7 and y = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
- Max@Math Revolution
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=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) and 2) together first.
Conditions 1) and 2):
y = 10 - x and xy= x(10-x) = 21
⇔ -x^2 + 10x = 21
⇔ x^2 - 10x + 21 = 0
⇔ (x-3)(x-7) = 0
⇔ x = 3 and y = 7, or x = 7 and y = 3.
Since x > y, we must have x = 7 and y = 3.
Thus x = 7, and conditions 1) and 2) are sufficient, when taken together.
Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT 4(A).
Condition 1)
There are two possible solutions: x = 6 and y = 4, and x = 7 and y = 3.
Since the solution is not unique, condition 1) is not sufficient.
Condition 2):
Either x = 3 and y = 7, or x = 7 and y = 3.
Since x > y, x = 7 and y = 3.
Thus, we have the unique solution, x = 7.
Therefore, condition 2) is sufficient.
Therefore, B is the answer.
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Answer: B
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) and 2) together first.
Conditions 1) and 2):
y = 10 - x and xy= x(10-x) = 21
⇔ -x^2 + 10x = 21
⇔ x^2 - 10x + 21 = 0
⇔ (x-3)(x-7) = 0
⇔ x = 3 and y = 7, or x = 7 and y = 3.
Since x > y, we must have x = 7 and y = 3.
Thus x = 7, and conditions 1) and 2) are sufficient, when taken together.
Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT 4(A).
Condition 1)
There are two possible solutions: x = 6 and y = 4, and x = 7 and y = 3.
Since the solution is not unique, condition 1) is not sufficient.
Condition 2):
Either x = 3 and y = 7, or x = 7 and y = 3.
Since x > y, x = 7 and y = 3.
Thus, we have the unique solution, x = 7.
Therefore, condition 2) is sufficient.
Therefore, B is the answer.
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Answer: B
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