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30 Apr 2020, 03:29
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:04) correct
31%
(02:03)
wrong
based on 248
sessions
History
Date
Time
Result
Not Attempted Yet
If A is an integer, what is the value of A?
(1) \(1,000,000 < 23^A < 10,000,000\)
(2) \(\frac{7^{A+2}−7^A}{48}=7^A\)
Are You Up For the Challenge: 700 Level Questions
(1) \(1,000,000 < 23^A < 10,000,000\)
(2) \(\frac{7^{A+2}−7^A}{48}=7^A\)
Are You Up For the Challenge: 700 Level Questions
30 Apr 2020, 03:41
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Bunuel
Question: A = ?
Statement 1: \(1,000,000 < 23^A < 10,000,000\)
\(23^2 = 529\)
\((23^2)^2 = 529^2 ≈ 500^2 ≈ 250,000\) i.e. Less than 1,000,000
\(23^5 = (23^2)^2*23 ≈ 250000*23 ≈ 6,250,000\)
i.e. between 1,000,000 and 10,000,000
\(23^6 ≈ 6250000*23 ≈ 14,000,000\) i.e. Greater than 10,000,000
i.e. A = 5
SUFFICIENT
Statement 2: \(\frac{7^{A+2}−7^A}{48}=7^A\)
i.e. \(7^A*(7^2-1) = 7^A*48\)
i.e. 48 = 48, No value fo A hence
NOT SUFFICIENT
ANswer: Option A
30 Apr 2020, 04:00
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Bunuel
(Statement1): \(10^{6} < 23^{A} < 10^{7}\)
\(23^{2}= 529\)
\(23^{4}= 529*529 > \frac{10^{3}}{2}* \frac{10^{3}}{2}= \frac{10^{6}}{4} < 10^{6}\)
\(23^{5} ≈ \frac{10^{6}}{4}* 23= 5.75* 10^{6} > 10^{6}\)
\(23^{6} ≈ 5.75* 10^{6}* 23= 5.75*2.3* 10^{7} > 10^{7}\)
Well, we got only one value of A satisfying the inequality
A=5
Sufficient
(Statement2): \(\frac{7^{A+2}−7^A}{48}=7^A\)
\(\frac{7^{A} (49 -1)}{48}= 7^{A}\)
--> \(7^{A} = 7^{A}\)
A could be any integer
Insufficient
Answer (A).
