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20 Jan 2019, 18:43
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[Math Revolution GMAT math practice question]
Is a > b - c?
1) |c-b| < a
2) a, b, and c are the lengths of the 3 sides of a triangle.
=>
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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Condition 1) is sufficient since it yields b – c ≤ | b - c | = | c – b | < a.
Condition 2)
Since the sum of the lengths of two sides of a triangle is greater than the length of the third side, we must have a + c > b. Thus, condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
Is a > b - c?
1) |c-b| < a
2) a, b, and c are the lengths of the 3 sides of a triangle.
=>
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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Condition 1) is sufficient since it yields b – c ≤ | b - c | = | c – b | < a.
Condition 2)
Since the sum of the lengths of two sides of a triangle is greater than the length of the third side, we must have a + c > b. Thus, condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
21 Jan 2019, 19:26
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[Math Revolution GMAT math practice question]
If x and y are integers, is x2-y2 an even integer?
1) x^3-y^3 is an even integer
2) x+y is an even integer
=>
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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Asking whether x^2-y^2 is even is equivalent to asking whether (x+y)(x-y) is an even integer.
Condition 2) is sufficient since x^2-y^2 = (x+y)(x-y) is an even integer if x + y is an even integer.
Condition 1)
In order for x^3-y^3 to be an even integer, x and y must both have the same parity.
There are only two cases to consider: both x and y are even integers or both are odd integers.
Since x and y have the same parity, x – y is always an even integer.
Thus, x^2-y^2 is an even integer. Condition 1) is sufficient.
Therefore, D is the answer.
Answer: D
If x and y are integers, is x2-y2 an even integer?
1) x^3-y^3 is an even integer
2) x+y is an even integer
=>
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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Asking whether x^2-y^2 is even is equivalent to asking whether (x+y)(x-y) is an even integer.
Condition 2) is sufficient since x^2-y^2 = (x+y)(x-y) is an even integer if x + y is an even integer.
Condition 1)
In order for x^3-y^3 to be an even integer, x and y must both have the same parity.
There are only two cases to consider: both x and y are even integers or both are odd integers.
Since x and y have the same parity, x – y is always an even integer.
Thus, x^2-y^2 is an even integer. Condition 1) is sufficient.
Therefore, D is the answer.
Answer: D
22 Jan 2019, 18:17
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[Math Revolution GMAT math practice question]
A sequence An satisfies An+3=An+8. What is the remainder when A99 is divided by 8?
1) A1=1
2) A2=2
=>
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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
The initial condition, An+3=An+8, tells us that every third term has the same remainder when it is divided by 8.
By condition 1), A1 = 1, A4 = 9, A7 = 17, … , A97 = 257, A100 = 265 …. Each of these terms has remainder 1 when it is divided by 8.
By condition 2), A2 = 2, A5 = 10, A8 = 18, … , A98 = 258, A101 = 266 …. Each of these terms has remainder 2 when it is divided by 8.
A99 does not appear in either of these lists. Thus, both conditions together do not provide enough information to find the remainder when A99 is divided by 8. Therefore, E is the answer.
Note: in order to find the remainder when A99 is divided by 8, we need the value of A3. Thus, we need the values of 3 variables, and we are given only 2, so E should be the answer.
Therefore, the correct answer is E.
Answer: E
A sequence An satisfies An+3=An+8. What is the remainder when A99 is divided by 8?
1) A1=1
2) A2=2
=>
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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
The initial condition, An+3=An+8, tells us that every third term has the same remainder when it is divided by 8.
By condition 1), A1 = 1, A4 = 9, A7 = 17, … , A97 = 257, A100 = 265 …. Each of these terms has remainder 1 when it is divided by 8.
By condition 2), A2 = 2, A5 = 10, A8 = 18, … , A98 = 258, A101 = 266 …. Each of these terms has remainder 2 when it is divided by 8.
A99 does not appear in either of these lists. Thus, both conditions together do not provide enough information to find the remainder when A99 is divided by 8. Therefore, E is the answer.
Note: in order to find the remainder when A99 is divided by 8, we need the value of A3. Thus, we need the values of 3 variables, and we are given only 2, so E should be the answer.
Therefore, the correct answer is E.
Answer: E
