If \(P344_{6} - 23P2_{6} = 2PP2_{6}\), find the value of the digit P.
2
3
4
5
Correct answer is D
Convert everything to base 10 and collect like terms, such that:
\(210P - 42P = 434 + 406\)
\(168P = 840\)
\(P = 840/168 = 5\)
Simplify \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\)
2n+1
2n-1
4
1/4
Correct answer is C
Start by expanding \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\):
\(\frac{3 \times 2^n \times 2^1 - 2^2 \times 2^n \times 2^{-1}}{2^n \times 2 - 2^n}\)
NUMERATOR : 2\(^n\) ( 3\(^1\) X 2\(^1\) - 2\(^2\) X 2\(^-1\) )
--> 2\(^n\) ( 3 X 2 — 4 X \(\frac{1}{2}\) )
--> 2\(^n\) ( 6 - 2 )
--> 2\(^n\) (4)
DENOMINATOR : 2\(^n\) ( 2\(^1\) - 1 )
--> 2\(^n\) ( 2 - 1)
--> 2\(^n\)
: [ 2\(^n\) ( 4) ] ÷ 2\(^n\)
= 4
If 314\(_10\) - 256\(_7\) = 340\(_x\), find x.
7
8
9
10
Correct answer is A
31410 - 2567 = 340x,
Convert 2567 and 340x to base 10, such that:
314 - 139 = 3x2 + 4x
=> 3x2 + 4x - 175 = 0 (quadratic)
Factorising, (x - 7) (3x + 25) = 0,
either x = 7 or x = -25/3 ( but x cannot be negative)
Therefore, x = 7.
N112,000.50
N96,000.00
N85,714.28
N76,800.00
Correct answer is D
Amount A = P(1+r)n;
A = N150,000, r = 25%, n = 3.
150,000 = P(1+0.25)3 = P(1.25)3
P = 150,000/1.253 =N76,800.00
0.056
0.055
0.054
0.54
Correct answer is B
\(\frac{2.813 \times 10^{-3} \times 1.063}{5.637 \times 10^{-2}}\)
= \(\frac{0.002813 \times 1.063}{0.05637}\)
\(\approxeq \frac{0.0028 \times 1.1}{0.056}\)
= \(0.055\)