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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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[Math Revolution GMAT math practice question]

Tom’s Mom is five times as old as him. In 6 years, Tom’s Mom will be three times as old as him. How old is Tom now?

A. 3
B. 4
C. 5
D. 6
E. 7

=>

We can set up this question using the IVY approach. “Is”
can be converted to “=” and “times” can be converted to the multiplication sign “x”.

Let m and t be Tom’s Mom’s age and Tom’s age now, respectively.
Then m = 5t since Tom’s mom is five times as old as Tom.
We also have
m + 6 = 3(t + 6) since Tom’s mom will be three times as old as Tom in 6 years.

Plugging m = 5t into the second equation yields
5t + 6 = 3t + 18 or 2t = 12.
So, t = 6.

Therefore, the answer is D.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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[Math Revolution GMAT math practice question]

Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If lines AB and BC are perpendicular to each other, p=?

A. -2
B. -1
C. 0
D. 1
E. 2

=>

The slope of the line segment joining the two points (x1,y1) and (x2,y2) is (y1-y2)/(x1-x2). The product of the slopes of perpendicular lines is -1.

The slope of the line AB is (4-2)/(1-2) = -2.
Since the two lines AB and BC are perpendicular each other, the slope of BC, which is (2-1)/(2-p), must be 1/2.
So,
(2-1)/(2-p)=1/2
1/(2-p)=1/2.
Thus, 2 – p = 2, and p = 0.

Therefore, the answer is C.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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[Math Revolution GMAT math practice question]

||2-3|-|2-5||=?

A. 1
B. 2
C. 3
D. 4
E. 5

=>

||2-3| - |2-5|| = ||-1| - |-3|| = | 1 – 3 | = | -2 | = 2.

Therefore, the answer is B.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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[Math Revolution GMAT math practice question]

What is the greatest prime factor of 1+2+3+….+36?

A. 2
B. 3
C. 9
D. 31
E. 37

=>

Since 1 + 2 + 3 + … + n = n(n+1)/2, we have 1 + 2 + 3 + … + 36 = (36*37)/2 = 18*37 = 2*32*37.
Thus, 37 is the greatest prime factor of 2*3^2*37.

Therefore, the answer is E.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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[Math Revolution GMAT math practice question]

The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. What is the area of the square?

A. 16
B. 25
C. 32
D. 36
E. 50

=>

The length of the diagonal of the square is √{ (7-1)^2 + (6-(-2))^2 } = √100 = 10.
The side-length of the square is 10/ √2 = 5 √2 since the side-length of a square is equal to the length of its diagonal divided by √2. Thus, the area of the square is (5 √2)^2 = 50.

Therefore, E is the answer.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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[Math Revolution GMAT math practice question]

If 2 numbers are selected from the first 8 prime numbers, what is the probability that the sum of the 2 numbers selected is an even number?

A. 1/2
B. 1/3
C. 2/3
D. 1/4
E. 3/4

=>

In order for the sum to be even, both primes selected must be odd. As 2 is the only even prime number, the number of selections with an even sum is equal to the number of ways to select 2 numbers from these 7 odd prime numbers, or 7C2.
The total number of selections of 2 prime numbers from the first 8 prime numbers is 8C2.
Therefore, the probability that the sum of the two numbers selected is even is
7C2 / 8C2 = {(7*6)/(1*2)}/{(8*7)/(1*2)} = 6/8 = 3/4.

Therefore, the answer is E.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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[Math Revolution GMAT math practice question]

If x+(1/x)=4, what is the value of x^2+(1/x^2)?

A. 4
B. 10
C. 12
D. 14
E. 16

=>
Since (a+b)^2=a^2+b^2+2ab, a^2+b^2=(a+b)^2-2ab, and
x^2 + 1/x^2 = ( x + 1/x )^2 – 2*x*(1/x) = 4^2 – 2 = 16 -2 = 14.

Therefore, the answer is D.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (PS)  [#permalink]

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[Math Revolution GMAT math practice question]

What is the solution of the equation (x-1)/(1-x) = 0?

A. -1
B. 0
C. 1
D. 0 or 1
E. The equation has no solution.

=>

In order for a fraction to be zero, its numerator must be 0. This occurs when x = 1. However, if x = 1, then the denominator of this fraction is 0. Thus, 0 is an erroneous solution, and the equation has no solution.

Therefore, the answer is E.
_________________ Re: Math Revolution Approach (PS)   [#permalink] 14 Oct 2018, 18:51

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