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15 Aug 2018, 18:19
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[Math Revolution GMAT math practice question]
If a, b, and c are consecutive 2-digit positive integers in that order, and a+b+c is a multiple of 10, what is the value of c?
1) a is a prime number
2) c is a prime number
=>
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.
Since a = b – 1 and c = b + 1, we have a + b + c = ( b – 1 ) + b + ( b + 1 ) = 3b is a multiple of 10 and b is a multiple of 10. Thus, the possible triples ( a, b, c ) are ( 19, 20, 21 ), ( 29, 30, 31 ), ( 39, 40, 41 ), ( 49, 50, 51 ), ( 59, 60, 61 ), ( 69, 70, 71 ), ( 79, 80, 81 ) and ( 89, 90, 91 ). Since we have 3 variables and 2 equations ( a = b – 1, c = b + 1), D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
The triples in which a is a prime number are
( 19, 20, 21 ), ( 29, 30, 31 ), ( 59, 60, 61 ), ( 79, 80, 81 ) and ( 89, 90, 91 ).
Thus, c could be 21, 31, 61, 81 or 91.
Since we don’t have a unique solution, condition 1) is not sufficient.
Condition 2)
The triples in which c is a prime number are
( 29, 30, 31 ), ( 39, 40, 41 ), ( 59, 60, 61 ), ( 69, 70, 71 ) and ( 89, 90, 91 ).
Thus, c could be 31, 41, 61, 71 or 91.
Since we don’t have a unique solution, condition 2) is not sufficient.
Conditions 1) & 2):
The triples in which both a and c are prime numbers are:
( 29, 30, 31 ), ( 59, 60, 61 ) and ( 89, 90, 91 ).
Thus, c could be 31, 61 or 91.
Since we don’t have a unique solution, both conditions are not sufficient, when considered together.
Therefore, E is the answer.
Answer: E
If a, b, and c are consecutive 2-digit positive integers in that order, and a+b+c is a multiple of 10, what is the value of c?
1) a is a prime number
2) c is a prime number
=>
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.
Since a = b – 1 and c = b + 1, we have a + b + c = ( b – 1 ) + b + ( b + 1 ) = 3b is a multiple of 10 and b is a multiple of 10. Thus, the possible triples ( a, b, c ) are ( 19, 20, 21 ), ( 29, 30, 31 ), ( 39, 40, 41 ), ( 49, 50, 51 ), ( 59, 60, 61 ), ( 69, 70, 71 ), ( 79, 80, 81 ) and ( 89, 90, 91 ). Since we have 3 variables and 2 equations ( a = b – 1, c = b + 1), D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
The triples in which a is a prime number are
( 19, 20, 21 ), ( 29, 30, 31 ), ( 59, 60, 61 ), ( 79, 80, 81 ) and ( 89, 90, 91 ).
Thus, c could be 21, 31, 61, 81 or 91.
Since we don’t have a unique solution, condition 1) is not sufficient.
Condition 2)
The triples in which c is a prime number are
( 29, 30, 31 ), ( 39, 40, 41 ), ( 59, 60, 61 ), ( 69, 70, 71 ) and ( 89, 90, 91 ).
Thus, c could be 31, 41, 61, 71 or 91.
Since we don’t have a unique solution, condition 2) is not sufficient.
Conditions 1) & 2):
The triples in which both a and c are prime numbers are:
( 29, 30, 31 ), ( 59, 60, 61 ) and ( 89, 90, 91 ).
Thus, c could be 31, 61 or 91.
Since we don’t have a unique solution, both conditions are not sufficient, when considered together.
Therefore, E is the answer.
Answer: E
16 Aug 2018, 18:10
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[Math Revolution GMAT math practice question]
x ≠ 0. Is x^2>x^4?
1) x^2<1
2) x^2<2x
=>
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.
x^2>x^4
=> x^4 - x^2 < 0
=> x^2 ( x^2 – 1 ) < 0
=> ( x^2 – 1 ) < 0
=> ( x + 1 )( x – 1 ) < 0
=> -1 < x < 1
This is equivalent to condition 1).
Thus, condition 1) is sufficient.
Condition 2)
x^2<2x
=> x^2 - 2x < 0
=> x(x – 2) < 0
=> 0 < x < 2
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
However, the solution set of the question -1 < x < 1 does not include the solution set of the condition, 0 < x < 2. Thus, condition 2) is not sufficient.
Therefore, A is the answer.
x ≠ 0. Is x^2>x^4?
1) x^2<1
2) x^2<2x
=>
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.
x^2>x^4
=> x^4 - x^2 < 0
=> x^2 ( x^2 – 1 ) < 0
=> ( x^2 – 1 ) < 0
=> ( x + 1 )( x – 1 ) < 0
=> -1 < x < 1
This is equivalent to condition 1).
Thus, condition 1) is sufficient.
Condition 2)
x^2<2x
=> x^2 - 2x < 0
=> x(x – 2) < 0
=> 0 < x < 2
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
However, the solution set of the question -1 < x < 1 does not include the solution set of the condition, 0 < x < 2. Thus, condition 2) is not sufficient.
Therefore, A is the answer.
19 Aug 2018, 18:47
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[Math Revolution GMAT math practice question]
If the average (arithmetic mean) of 3 integers x, y, z is 10, what is the value of z?
1) x=1
2) x=5-y
=>
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 original condition gives ( x + y + z ) / 3 = 10 or x + y + z = 30. Rearranging yields z = 30 – ( x + y ). Condition 2) gives x + y = 5, so condition 2) is sufficient .
Condition 1) is not sufficient since it gives no information about the value of y.
Therefore, B is the answer.
Answer: B
If the average (arithmetic mean) of 3 integers x, y, z is 10, what is the value of z?
1) x=1
2) x=5-y
=>
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 original condition gives ( x + y + z ) / 3 = 10 or x + y + z = 30. Rearranging yields z = 30 – ( x + y ). Condition 2) gives x + y = 5, so condition 2) is sufficient .
Condition 1) is not sufficient since it gives no information about the value of y.
Therefore, B is the answer.
Answer: B
