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10 Aug 2018, 02:35
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[Math Revolution GMAT math practice question]
If x, y, z are positive integers and x<y<z, which of the following must be greater than (z^x)(z^y)?
A. y^{2z}
B. y^{2y}
C. x^{2y}
D. x^{zx}
E. z^{2y}
=>
Since z^x < z^y, we have (z^x)(z^y)< (z^y)(z^y) = z^{2y}.
Therefore, the answer is E.
Answer: E
If x, y, z are positive integers and x<y<z, which of the following must be greater than (z^x)(z^y)?
A. y^{2z}
B. y^{2y}
C. x^{2y}
D. x^{zx}
E. z^{2y}
=>
Since z^x < z^y, we have (z^x)(z^y)< (z^y)(z^y) = z^{2y}.
Therefore, the answer is E.
Answer: E
13 Aug 2018, 06:27
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[Math Revolution GMAT math practice question]
he lengths of two sides of a certain obtuse triangle are 9 and 12. Which of the following could be the length of the third side of the triangle?
A. 12
B. 13
C. 14
D. 15
E. 16
=>
If a, b and c are sides of a right triangle and c is the longest side, then c^2 = a^2 + b^2.
If a, b and c are sides of an acute triangle and c is the longest side, then c^2 < a^2 + b^2.
If a, b and c are sides of an obtuse triangle and c is the longest side, then c^2 > a^2 + b^2.
Since 15^2 = 9^2 + 12^2 and 16 > 15, 16 could be the third side of the obtuse triangle.
Therefore, the answer is E.
Answer : E
he lengths of two sides of a certain obtuse triangle are 9 and 12. Which of the following could be the length of the third side of the triangle?
A. 12
B. 13
C. 14
D. 15
E. 16
=>
If a, b and c are sides of a right triangle and c is the longest side, then c^2 = a^2 + b^2.
If a, b and c are sides of an acute triangle and c is the longest side, then c^2 < a^2 + b^2.
If a, b and c are sides of an obtuse triangle and c is the longest side, then c^2 > a^2 + b^2.
Since 15^2 = 9^2 + 12^2 and 16 > 15, 16 could be the third side of the obtuse triangle.
Therefore, the answer is E.
Answer : E
13 Aug 2018, 06:29
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[Math Revolution GMAT math practice question]
In the x-y coordinate plane, the distance between (p,q) and (1,1) is 5. If p and q are integers, how many possibilities are there for the point (p,q)?
A. 2
B. 4
C. 8
D. 12
E. 16
=>
(p-1)^2 + (q-1)^2 = 5^2
If p – 1 = ±3, and q - 1 = ±4, then p = 1 ± 3, and q = 1 ± 4. There are four possible points: ( p, q ) = ( 4, 5 ), ( 4, -3 ), ( -2, 5 ), ( -2, -3 ).
If p – 1 = ±4, and q - 1 = ±3, then p = 1 ±4, and q = 1 ± 3. There are four possible points: ( p, q ) = ( 5, 4 ), ( 5, -2 ), ( -3, 4 ), ( -3, -2 ).
If p – 1 = 0, and q - 1 = ±5, then p = 1, and q = 1 ±5. There are two possible points: ( p, q ) = ( 1, 6 ), ( 1, -4 ).
If p – 1 = ±5, and q - 1 = 0, then p – 1 = ±5, and q = 1. There are two possible points: ( p, q ) = ( 6, 1 ), ( -4, 1 ).
There are a total of 4 + 4 + 2 + 2 = 12 possibilities for the point (p,q).
Therefore, the answer is D.
Answer: D
In the x-y coordinate plane, the distance between (p,q) and (1,1) is 5. If p and q are integers, how many possibilities are there for the point (p,q)?
A. 2
B. 4
C. 8
D. 12
E. 16
=>
(p-1)^2 + (q-1)^2 = 5^2
If p – 1 = ±3, and q - 1 = ±4, then p = 1 ± 3, and q = 1 ± 4. There are four possible points: ( p, q ) = ( 4, 5 ), ( 4, -3 ), ( -2, 5 ), ( -2, -3 ).
If p – 1 = ±4, and q - 1 = ±3, then p = 1 ±4, and q = 1 ± 3. There are four possible points: ( p, q ) = ( 5, 4 ), ( 5, -2 ), ( -3, 4 ), ( -3, -2 ).
If p – 1 = 0, and q - 1 = ±5, then p = 1, and q = 1 ±5. There are two possible points: ( p, q ) = ( 1, 6 ), ( 1, -4 ).
If p – 1 = ±5, and q - 1 = 0, then p – 1 = ±5, and q = 1. There are two possible points: ( p, q ) = ( 6, 1 ), ( -4, 1 ).
There are a total of 4 + 4 + 2 + 2 = 12 possibilities for the point (p,q).
Therefore, the answer is D.
Answer: D
