GRE Math

A farmer has 34ft of fence, and wants to fence in his sheep. He wants to build a rectangular pen with one side formed by the side of his barn. He wants the area of the pen to be 120ft². Which of the following is a possible dimension? 7ft, 10ft, 22ft, 30ft?

120=xy and 34=2x+y Substitute 34=2x+120/x 34x=2x²+120 0=2x²-34x+120 x²-17x+60 Factor (x-5)(x-12)=0 x= 5 or 12=the side NOT opposite the barn y=120/5=24 or y=120/12=10 10ft! since 24 is not an option

A given university has an average professor pay of $40000 a year and an average administrator pay of $45000 per year. If the ratio of professors to administrators is 4 to 3, and the total pay for professors and administrators in a year is $40415000, how many professors does the college have?

40000p+45000a=40415000 p/a=4/3 Solve and substitute a=3/4p 40000p+45000(3/4p)=40415000 40000p+33750p=40415000 73750p=40415000 p=548

A theme park charges $10 for adult tickets and $5 for kids. How many kids tickets were sold if a total of 548 tickets were sold for a total of $3750?

5c+10(548-c)=3750 5c+5480-10c=3750 5c+1730=10c 1730=5c 346=c

If (7/8)ⁿ=√(7/8)⁵, what is n?

Convert √ to ∧½. Now 7/8 is being raised to the 5th power and ½ power at the same time. Multiply them together to get n. n=5x½=5/2.

One of the roots of the equation x²+kx-12=0 is 3. K is a constant. Which is greater, the value of k or -1?

Factor the equation: x²+kx-12=0 x-3=0 x=3 We know the other root is -4, because -12÷3=-4. kx=4x-3x 3k=4(3)-3(3) 3k=12-9 3k=3 k=1 The value of k is greater then -1

A circle is inscribed within the boundaries of a square. If r=5, what is the area of the upper corner of the square?

Find the length of the side of the square D=2r=2*5=10 Area of square=d²=10²=100 Area of circle=πr²=π5²=25π Area of 4 corners=100-25π Area of 1 corner=(100-25π)/4 Simplify =25-(25/4)*π

What is the length of the arc of a circle with radius 10 that traces a 50 degree angle?

Length of arc=(degrees*2πr)/360 =(50*2π*10)/360 =1000π/360 =25π/9

Jon invested part of $16000 at 3% and the rest at 5% for a total return of $680. Which is greater, the amount at 3% or at 5%?

Let x represent the amount at 3%: .03x+.05(16000-x)=680 Sove for x. x=6000 y=16000-x=10000 y is greater aka 5% is greater

Kim is twice as old as Claire. Nick is 3 years older then Claire. Kim is 6 years older then Emily. Their ages combined equal 81. How old is Nick?

N=c+3, K=2c, E=2c-6 c+3+2c+2c-6+c=81 6c-3=81 6c=84 c=14 N=14+3 N=17

(bxb⁴xb⁷)∧½/(b³xb⁺)=b⁵. Solve for +. Is it -1, -2, 3 or 1?

Simplify. (b12)∧½/(b³⁺⁺)=b⁵ b⁶/b³⁺⁺=b⁵ Then plug and chug. -2 fits this equation best.

There are two lines: 2x-4y=33 2x+4y=33 Are these lines perpendicular, parallel, non-perpendicular intersecting, or the same line?

Solve both lines: 2x-4y=33 y=½x-33/4 2x+4y=33 y=-½x+33/4 They are not the same line. They are not parallel because they do not have the same slope. They are not perpendicular because the slope would need to be opposite (which they are) and reciprocal (they are not). They are not perpendicular intersecting.

x+y=12 and 2x-y=6 Which is greater, x or y?

Solve for y and substitute. y=12-x 2x-(12-x)=6 2x-12+x=6 3x=18 x=6 Now fill x back in to original equation to solve for y y=12-6=6 Both quantities are equal

Sarah's current age is 3 times Ron's age two years ago. Sarah is currently 14 years older than Ron. What is the sum of Sarah and Ron's current age?

Turn into equations: s=3(r-2) and s=14+r Substitute 14+r=3(r-2) r=3r-6-14 -2r=-20 r=10 Solve for s s=14+10=24 Sum of ages=10+24=34

What digit appears in the units place when 2¹⁰² is multiplied out?

Unit place of the first few powers of 2: 2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁵=32. Take the numbers in the 1 unit of the answers and you get a sequence of 2, 4, 8, 6...which is a sequence of 4 digits. Divide 102 by 4 BY HAND and you get 25 with a remainder of 2. The second number in the sequence is 4, so the answer is 4.

Bill and Bob are working to build toys. Bill can build k toys in 6 hours. Bob can build k toys in 3 hours. How long would it take Bob and Bill to build 4k toys working together?

k/6+k/3=k/2 k/6+2k/6=3k/6 plug in numbers 2/6+4/6=6/6 TRUE 4k=hours 4(2)=8 8 hours

Let n be a prime integer such that one less than 3/8s of n is the third prime integer. What is n?

n=(5+1)x(8/3)=16