Improve your scores with Capstone’s GRE Practice of the Day. Get GRE practice questions with detailed solutions – delivered into your inbox. Study consistent. Study smart.
In order to compare the two quantities A and B, we need to make either the bases the same (so that we can compare the indices) or make the indices (exponents) the same (and compare the bases). 2 and 3 are prime numbers so the bases will never be the same, let’s equate the indices and then compare the bases to see which is larger.
215 = (23)5 and 310 = (32)5
QUANTITY A = 85
QUANTITY B = 95
Quantity B is greater.
First, let’s look at the standard school method of solving this question.
Let the original price be x
In 2008, the list price of a home was 1/3 greater than the original price = x + x/3 = 4x/3
In 2018, the list price of the home was 1/2 greater than the original price = x + x/2 = 3x/2
Increase = 3x/2 – 4x/3 = x/6
Percent increase from 2008 to 2018 = (x/6 ÷ 4x/3) x 100 = 12.5%.
If working with fractions is cumbersome for you, then here’s another solution.
Let the original price be 300 (or any number that can be easily divided by both 3 and 2)
In 2008, the list price of a home was 1/3 greater than the original price = 300 + (300/3) = 400
In 2018, the list price of the home was 1/2 greater than the original price = 300 + (300/2) = 450
Increase = 450 – 400 = 50
Percent increase from 2008 to 2018 = (50/400) x 100 = 12.5%.
Each of the photograph’s sides measures x inches, area of photograph = x2.
Length of outer square (photograph + frame) = x + 3+ 3 = x + 6
Area of photograph + frame = (x+6)2
If the frame and the picture have the same area, then
Area of photograph + frame = 2 x Area of photograph
(x+6)2 = 2x2
Observe how the points (4.3) and (11,3) are in a straight line and so are (4,3) and (4,9), which means we can save some time and not use the distance formula. A rough sketch would be useful.
OQ = 6 units (9-3=6) and is inside the circle hence smaller than the radius.
OP = 7 units (9-3=6) and is outside the circle hence larger than the radius.
So the radius is more than 6 units but less than 7 units. Only possible answer is 6.5 units.
Get GRE Ready. Practice Questions with Solutions delivered to your inbox.
Get GRE ready. 30 minutes a day.