Source: Official Guide for GMAT Review 2016 Problem Solving; #57

1

Which of the following expressions can be written

Which of the following expressions can be written as an integer? I.(82 + 82) ^2 II. (82)(82) III.(82)(82)/82

1 Explanation

1

John Robertson

I) (SQR(82)+SQR(82))^2
-> You could foil it out, but a radical times itself, or a radical squared, cancels out the radical leaving just the integer inside (not the most elegant math explanation though). Since both expressions in ( ....) are radicals, you'll be multiplying a bunch of radicals times themselves, it'll equal a bunch of integers added together, which would equal an integer (vs. if it was (SQR(82)+4), then you'd have to solve it out and see bc one result of foil would be 4xSQR(82), for example).

II) 82x(SQR(82))
-> 82^1 x 82^(1/2) = 82 ^ (3/2) = SQR(82^3) = SQR (41^3) x SQR (2^3), neither are perfect squares to simplify to x^3, not an integer.

III) (SQR(82)xSQR(82))/82, numerator follows same rules as (I), simplifies to 82, 82/82 =1, integer.

ANS: I and III, E

Feb 23, 2017 • Comment

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