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24 Oct 2018, 18:23
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[Math Revolution GMAT math practice question]
If a rectangle’s length is a+b and its area is (1/a)+(1/b), what is its width?
A. 1
B. a+b
C. ab
D. 1/(a+b)
E. 1/ab
=>
Let x be the width of the rectangle. Then
x(a+b) = 1/a + 1/b = (a+b)/ab.
Thus, x = 1/ab.
Therefore, the answer is E.
Answer: E
If a rectangle’s length is a+b and its area is (1/a)+(1/b), what is its width?
A. 1
B. a+b
C. ab
D. 1/(a+b)
E. 1/ab
=>
Let x be the width of the rectangle. Then
x(a+b) = 1/a + 1/b = (a+b)/ab.
Thus, x = 1/ab.
Therefore, the answer is E.
Answer: E
25 Oct 2018, 18:18
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[Math Revolution GMAT math practice question]
In the xy-plane, does the graph of y=ax^2+c intersect the x-axis?
1) a>0
2) c>0
=>
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 question “does the graph of y=ax^2+c intersect the x-axis” is equivalent to asking “does the equation ax^2+c = 0 have a root”.
Note that the statement “ax^2 + bx + c = 0 has a root” is equivalent to b^2-4ac ≥ 0.
Thus, the question asks if -4ac ≥ 0, or ac ≤ 0, since b = 0 in this problem.
When we consider both conditions together, we obtain ac > 0 and the answer is “no”, since a > 0 and c > 0.
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, both conditions together are sufficient.
Note: Neither condition on its own provides enough information for us to determine whether ac ≤ 0.
Therefore, C is the answer.
Answer: C
In the xy-plane, does the graph of y=ax^2+c intersect the x-axis?
1) a>0
2) c>0
=>
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 question “does the graph of y=ax^2+c intersect the x-axis” is equivalent to asking “does the equation ax^2+c = 0 have a root”.
Note that the statement “ax^2 + bx + c = 0 has a root” is equivalent to b^2-4ac ≥ 0.
Thus, the question asks if -4ac ≥ 0, or ac ≤ 0, since b = 0 in this problem.
When we consider both conditions together, we obtain ac > 0 and the answer is “no”, since a > 0 and c > 0.
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, both conditions together are sufficient.
Note: Neither condition on its own provides enough information for us to determine whether ac ≤ 0.
Therefore, C is the answer.
Answer: C
28 Oct 2018, 19:20
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[Math Revolution GMAT math practice question]
n is an integer. Is n(n+2) a multiple of 8?
1) n is an even integer
2) n is a multiple of 4
=>
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.
Note that the product of two consecutive even integers is a multiple of 8 since one of them is a multiple of 4 and the other is an even integer.
Thus, each of conditions is sufficient since each implies that n and n+2 are two consecutive even integers.
Therefore, D is the answer.
Answer: D
n is an integer. Is n(n+2) a multiple of 8?
1) n is an even integer
2) n is a multiple of 4
=>
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.
Note that the product of two consecutive even integers is a multiple of 8 since one of them is a multiple of 4 and the other is an even integer.
Thus, each of conditions is sufficient since each implies that n and n+2 are two consecutive even integers.
Therefore, D is the answer.
Answer: D
