CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
The value of (2^(n+3) − 2^(n+1)) ÷ (2^(n+2) − 2^n) is:
The value is 2. Factor out 2^n: the numerator becomes 2^n(8 − 2) = 6·2^n and the denominator becomes 2^n(4 − 1) = 3·2^n. The common factor cancels, leaving 6/3 = 2, independent of n.
- A1
- B2Correct
- C3
- D4
Explanation
Numerator: 2^n(8 − 2) = 6·2^n. Denominator: 2^n(4 − 1) = 3·2^n. Ratio = 6/3 = 2. Check with n = 0: (8 − 2)/(4 − 1) = 2. Option 3 results from wrongly treating 8 − 2 as 3.
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