Problem Solving

swerve wrote:Which of the following is closest to the value of (2^23)(5^26)?

A. 10^23
B. 10^24
C. 10^25
D. 10^26
E. 10^27

(2^23)(5^26) = (2^23)(5^23)(5^3)
= (2^23)(5^23)(5^3)
= (10^23)(5^3)
= (10^23)(125)
≈ (10^23)(100)
≈(10^23)(10^2)
≈10^25

Answer: C

Cheers,
Brent

swerve wrote:Which of the following is closest to the value of (2^23)(5^26)?

A. 10^23
B. 10^24
C. 10^25
D. 10^26
E. 10^27

We can break 5^26 into two parts: 5^23 x 5^3 and then combine 5^23 with 2^23, as shown:
2^23 x 5^23 x 5^3

10^23 x 5^3 = 10^23 x 125, which is about 10^23 x 10^2 = 10^25.

Answer: C

Hi All,

We're asked which of the following is closest to the value of (2^23)(5^26). If you don't immediately see the 'Exponent' rules that apply to this question, then you can still solve it with some basic Arithmetic and logic.

To start, when you multiply a bunch of numbers together, the 'order' does NOT matter. For example (2)(3)(5) = 30 and (3)(5)(2) = 30. With the same numbers, any order will lead to the same result when you multiply.

In this question, we're multiplying a lot of 2s and a lot of 5s together... again though, the order doesn't matter. If we take one 2 and one 5 and multiply them, we get (2)(5) = 10. You should see pretty quickly that taking all twenty-three 2s and twenty-three of the 5s would give us twenty-three 10s all multiplied together... AND three "left over" 5s.

So far, that's (10^23)(5)(5)(5).... the product of those three 5s is (5)(5)(5) = 125...

(10^23)(125) is a bit more than (10^23)(100)... meaning that it's fairly close to (10^23)(10)(10) = 10^25

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

swerve wrote:Which of the following is closest to the value of (2^23)(5^26)?

A. 10^23
B. 10^24
C. 10^25
D. 10^26
E. 10^27

We can rewrite the expression as:

2^23 x 5^23 x 5^3

10^23 x 5^3

Since 5^3 = 125, which is close to 100, or 10^2, we have:

10^23 x 10^2 = 10^25

Answer: C