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27 Jan 2019, 18:31
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[Math Revolution GMAT math practice question]
If y=|x-1|+|x+1|, then y=?
1) x>-1
2) x<1
=>
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.
There are three ranges of values of x to consider.
If x > 1, then y = | x – 1 | + | x + 1 | = x – 1 + x + 1 = 2x and we don’t have a unique value of y.
If -1 ≤ x ≤ 1, then y = | x – 1 | + | x + 1 | = - ( x – 1 ) + x + 1 = 2 and we have a unique value of y.
If x < 1, then y = | x – 1 | + | x + 1 | = -( x – 1 ) – ( x + 1 ) = -2x and we don’t have a unique value of y.
Asking for the value of y is equivalent asking if -1 ≤ x ≤ 1.
Both conditions yield the inequality -1 < x < 1, when applied together. Therefore, both conditions are sufficient, when taken together.
In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient.
Therefore, C is the answer.
Answer: C
If y=|x-1|+|x+1|, then y=?
1) x>-1
2) x<1
=>
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.
There are three ranges of values of x to consider.
If x > 1, then y = | x – 1 | + | x + 1 | = x – 1 + x + 1 = 2x and we don’t have a unique value of y.
If -1 ≤ x ≤ 1, then y = | x – 1 | + | x + 1 | = - ( x – 1 ) + x + 1 = 2 and we have a unique value of y.
If x < 1, then y = | x – 1 | + | x + 1 | = -( x – 1 ) – ( x + 1 ) = -2x and we don’t have a unique value of y.
Asking for the value of y is equivalent asking if -1 ≤ x ≤ 1.
Both conditions yield the inequality -1 < x < 1, when applied together. Therefore, both conditions are sufficient, when taken together.
In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient.
Therefore, C is the answer.
Answer: C
29 Jan 2019, 21:44
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[Math Revolution GMAT math practice question]
m+n=?
1) (4^m)(2^n)=16
2) (2^{2m})(4^n)=64
=>
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 2) is equivalent to m + n = 3 as shown below:
(2^{2m})(4^n)=64
=> (2^{2m})(2^{2n})=2^6
=> 2^{2m+2n}=2^6
=> 2m+2n = 6
=> m + n = 3
Condition 2) is sufficient.
Condition 1)
(4^m)(2^n)=16
=> (2^{2m})(2^n)=2^4
=> 2^{2m+n}=2^4
=> 2m+n = 4
If m = 1 and n =2, then m + n = 3.
If m = 0 and n = 4, then m + n = 4.
Since it does not yield a unique solution, condition 1) is not sufficient.
Therefore, the answer is B.
Answer: B
m+n=?
1) (4^m)(2^n)=16
2) (2^{2m})(4^n)=64
=>
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 2) is equivalent to m + n = 3 as shown below:
(2^{2m})(4^n)=64
=> (2^{2m})(2^{2n})=2^6
=> 2^{2m+2n}=2^6
=> 2m+2n = 6
=> m + n = 3
Condition 2) is sufficient.
Condition 1)
(4^m)(2^n)=16
=> (2^{2m})(2^n)=2^4
=> 2^{2m+n}=2^4
=> 2m+n = 4
If m = 1 and n =2, then m + n = 3.
If m = 0 and n = 4, then m + n = 4.
Since it does not yield a unique solution, condition 1) is not sufficient.
Therefore, the answer is B.
Answer: B
31 Jan 2019, 17:31
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[Math Revolution GMAT math practice question]
What is the measure of each interior angle of a regular decagon?
A. 72°
B. 108°
C. 120°
D. 135°
E. 144°
=>
The sum of all interior angles of n-gon is (n-2)*180°.
A decagon is a 10-gon.
The sum of all interior angles is (10-2)* 180° = 8*180°.
And each interior angle of a regular decagon has measure 8*180° / 10 = 8*18° = 144°.
Therefore, the answer is E.
Answer: E
What is the measure of each interior angle of a regular decagon?
A. 72°
B. 108°
C. 120°
D. 135°
E. 144°
=>
The sum of all interior angles of n-gon is (n-2)*180°.
A decagon is a 10-gon.
The sum of all interior angles is (10-2)* 180° = 8*180°.
And each interior angle of a regular decagon has measure 8*180° / 10 = 8*18° = 144°.
Therefore, the answer is E.
Answer: E
