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Question Detail
Evaluate
\begin{aligned} \frac{10.3 \times 10.3 \times 10.3 + 1}{10.3 \times 10.3 - 10.3 + 1}
\end{aligned}
- 113
- 1.13
- 11.3
- 113
Answer: Option C
Explanation:
\begin{aligned}
a^3 + b^3 = (a+b)(a^2 + b^2 - ab)
\end{aligned}
\begin{aligned}
= \frac{10.3^3 + 1^3}
{10.3^2 + 1^2 - 10.3 \times 1}
\end{aligned}
\begin{aligned}
= (a+b) = (10.3+1) = 11.3
\end{aligned}
1. \begin{aligned}
(0.34\overline{67} + 0.13\overline{33}) = ?
\end{aligned}
- \begin{aligned} 0.048\overline{01} \end{aligned}
- \begin{aligned} 4.8\overline{01} \end{aligned}
- \begin{aligned} 48.\overline{01} \end{aligned}
- \begin{aligned} 0.48\overline{01} \end{aligned}
Answer: Option D
Explanation:
\begin{aligned}
(0.34\overline{67} + 0.13\overline{33})\end{aligned}
\begin{aligned} =
\frac{3467-34}{9900} + \frac{1333-13}{9900}
\end{aligned}
\begin{aligned}
= \frac{3433 + 1320}{9900}
= \frac{4753}{9900}
\end{aligned}
\begin{aligned}
= \frac{4801 - 48}{9900}
= 0.48\overline{01}
\end{aligned}
2. Evaluate
\begin{aligned}
3.\overline{14}
\end{aligned}
- \begin{aligned} 3\frac{14}{99} \end{aligned}
- \begin{aligned} \frac{14}{99} \end{aligned}
- \begin{aligned} 3\frac{14}{90} \end{aligned}
- \begin{aligned} 3\frac{1400}{99} \end{aligned}
Answer: Option A
Explanation:
when there is bar above a number, we can simplify it by dividing with 9's (equal to the number below bar, in this question 2 digits are below bar)
3. If 144/0.144 = 14.4/x, then x = ?
- 0.144
- 0.0144
- .00144
- 1.44
Answer: Option B
4. What will be the vulgar fraction of 0.75
- 3/5
- 3/4
- 3/2
- 3/7
Answer: Option B
Explanation:
0.75 = 75/100 = 3/4
5. Arrange fractions in descending order
- 9/11 > 8/9 > 3/5 > 4/7
- 9/11 > 8/9 > 4/7 > 3/5
- 8/9 > 9/11 > 3/5 > 4/7
- 9/11 >3/5 > 8/9 > 4/7
Answer: Option C
Explanation:
9/11 = .818 , 8/9 = .88 , 3/5 = .6, 4/7 = .571
So order is 8/9 > 9/11 > 3/5 > 4/7
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