Which of the following is closest to the value of (2^23)

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sat Nov 10, 2018 11:15 am

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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

The OA is C.

Source: Veritas Prep

Source: Beat The GMAT — Problem Solving | Sat Nov 10, 2018 11:15 am

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by Brent@GMATPrepNow » Sat Nov 10, 2018 4:27 pm

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)
â‰ˆ (10^23)(100)
â‰ˆ(10^23)(10^2)
â‰ˆ10^25

Answer: C

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Brent

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Sun Nov 11, 2018 6:06 am

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
Source: Veritas Prep

\[{2^{23}} \cdot {5^{26}}\,\, \cong \,\,\,{10^{\,?}}\,\]
\[{2^{23}} \cdot {5^{26}} = {2^{23}} \cdot {5^{23}} \cdot {5^3} = \,\,\,125\,\,{\left( {10} \right)^{23}}\]
\[\underline {1 \cdot {{10}^{25}}} = 100 \cdot {\left( {10} \right)^{23}} < \underline {125\,\,{{\left( {10} \right)}^{23}}} < 200 \cdot {\left( {10} \right)^{23}} = \underline {2 \cdot {{10}^{25}}} \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( C \right)\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8132; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Jan 21, 2019 6:15 pm

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

Scott Woodbury-Stewart
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by [email protected] » Tue Jan 22, 2019 10:46 am

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8132; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Jan 27, 2019 6:15 pm

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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