boomgoesthegmat wrote:Which of the following expressions can be written as an integer?

I. (√82 + √82)²
II. (82)(√82)
III. (√82)(√82)/82

A) None
B) I only
C) III only
D) I and II
E) I and III

OA: E

We'll use the fact that (√82)(√82) = 82

I. (√82 + √82)² = (2√82)² = (2√82)(2√82) = (2)(2)(√82)(√82) = (4)(82) = some integer
III. (√82)(√82)/82 = 82/82 = 1

NOTE: As we're checking expressions, we should also be checking the answer choices.
Since I and III both work, the correct answer must be E, since there's no option for all 3 to be true.

Cheers,
Brent

boomgoesthegmat wrote:Which of the following expressions can be written as an integer?

I. (sqrt82 + sqrt82)^2
II. (82)(sqrt82)
III. (sqrt82)(sqrt82)/82

A) None
B) I only
C) III only
D) 1 and II
E) I and III

Let's simplify each expression:

1. (√82 + √82)^2

(√82 + √82)^2 = (2√82)^2 = 4 x 82 = 328

We see that this an integer.

2. 82√82

Since √82 is a non-terminating decimal, 82√82 is not an integer.

3. (√82√82)/82

(√82√82)/82 = 82/82 = 1

We see that this is an integer.

Answer: E

Hi All,

We’re asked which of the following Roman Numerals can be written as an INTEGER.

While Roman Numeral questions can sometimes be time-consuming, this one is relatively straight-forward and is built on a couple of Number Property rules that can help you to avoid doing heavy calculations. You also do not need to consider all 3 Roman Numerals to answer it…

First, it’s worth noting that 82 is NOT a Perfect Square (if you know your Perfect Squares at this point, then you know that 9x9 = 81 and 10x10 = 100 are the two Squares just ‘below’ and ‘above’ 82, respectively).

I.

Adding any two identical terms together can be rewritten as 2(that term). For example, 3 + 3 = 2(3)…. X + X = 2(X)…. Etc.

Here, we’re adding root-82 to root-82, so that’s 2(root-82). Squaring that term would give us (2)(2)(82)… which is clearly an INTEGER (it’s 328, but you don’t actually have to do that math).

III.

Here, we are multiplying the same Square Root against itself – and any time you do that, you end up with the original integer. For example (root-4)(root-4) = (2)(2) = 4… (root-5)(root-5) = 5… Etc.

Thus, we would end up with 82 in the numerator and 82 in the denominator – and 82/82 = 1. This also is clearly an INTEGER.

Based on how the Answers are written, we can stop working.

Final Answer: E

GMAT Assassins aren’t born, they’re made,
Rich