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Louis14
Joined: 01 Nov 2019
Last visit: 04 Nov 2023
Posts: 249
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
GPA: 3.56
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Difficulty:
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74% (02:29) correct
26%
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If n is an integer, m = 6.3 × 10^(2n), and k = 0.9 × 10^n, what is the value of n?
(1) 0.05 < m/k < 0.5
(2) k < 0.02
(1) 0.05 < m/k < 0.5
(2) k < 0.02
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
Posts: 60
Louis14
Stat (1)
Use the definitions of m and k to write out \(\frac{m}{k}\).
→ \(\frac{m}{k} = \frac{6.3 × 10^{2n}}{0.9 × 10^n} = 7 × 10^{2n-n} = 7 × 10^n\)
Since n is an integer, this could be 7, 0.7, 0.07, 0.007, etc. The only way it will be between 0.05 and 0.5 is if it is 0.07 i.e. when n = -2.
Sufficient
Stat (2)
k will be less than 0.02 if it equals 0.009, 0.0009, etc. So, there are multiple possible values of n.
Insufficient
(a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Statement 1 -
\(\frac{m}{k} = \frac{6.3× 10^{2n}}{0.9 × 10^n} = 7 × 10^n\)
\(0.05 < 7 × 10^n < 0.5\)
or \(7 × 10^n = 0.07 \) (since n is an integer)
n= -2
Sufficient
Statement 2
\(0.9 × 10^n < 0.02\)
n<-1
insufficient
\(\frac{m}{k} = \frac{6.3× 10^{2n}}{0.9 × 10^n} = 7 × 10^n\)
\(0.05 < 7 × 10^n < 0.5\)
or \(7 × 10^n = 0.07 \) (since n is an integer)
n= -2
Sufficient
Statement 2
\(0.9 × 10^n < 0.02\)
n<-1
insufficient
Louis14
If n is an integer, m = 6.3 × 10^{2n}, and k = 0.9 × 10^n, what is the value of n?
\(\frac{6.3 * 10^{2n} }{ 0.9 * 10^n} = 0.7 *10^{2n-n} = 0.7 *10^n\)
(1) 0.05 < m/k < 0.5
0.05 < 0.07 < 0.5
N = - 2. Sufficient.
(2) k < 0.02[/quote]
N could have different values; insufficient.
Answer is A.
\(\frac{6.3 * 10^{2n} }{ 0.9 * 10^n} = 0.7 *10^{2n-n} = 0.7 *10^n\)
(1) 0.05 < m/k < 0.5
0.05 < 0.07 < 0.5
N = - 2. Sufficient.
(2) k < 0.02[/quote]
N could have different values; insufficient.
Answer is A.
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