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
Which of the following is closest to the value of (2^23)
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(2^23)(5^26) = (2^23)(5^23)(5^3)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)(5^23)(5^3)
= (10^23)(5^3)
= (10^23)(125)
≈ (10^23)(100)
≈(10^23)(10^2)
≈10^25
Answer: C
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\[{2^{23}} \cdot {5^{26}}\,\, \cong \,\,\,{10^{\,?}}\,\]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
\[{2^{23}} \cdot {5^{26}} = {2^{23}} \cdot {5^{23}} \cdot {5^3} = \,\,\,125\,\,{\left( {10} \right)^{23}}\]
\[\underline {1 \cdot {{10}^{25}}} = 100 \cdot {\left( {10} \right)^{23}} < \underline {125\,\,{{\left( {10} \right)}^{23}}} < 200 \cdot {\left( {10} \right)^{23}} = \underline {2 \cdot {{10}^{25}}} \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( C \right)\]
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
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We can break 5^26 into two parts: 5^23 x 5^3 and then combine 5^23 with 2^23, as shown: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 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
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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
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
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We can rewrite the expression as: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 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
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