Select Page
• This is an assessment test.
• These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
• Kindly take the tests in this series with a pre-defined schedule.

## Basic Maths: Test 52

Congratulations - you have completed Basic Maths: Test 52.

You scored %%SCORE%% out of %%TOTAL%%.

Your performance has been rated as %%RATING%%

 Question 1
The simplified value of $\left( 1-\frac{1}{5} \right)\,\left( 1-\frac{1}{6} \right)\,\left( 1-\frac{1}{7} \right)\,......\left( 1-\frac{1}{49} \right)\,\left( 1-\frac{1}{50} \right)$<br> is
 A $\frac{2}{25}$ B $\frac{1}{25}$ C $\frac{1}{50}$ D $\frac{1}{100}$
Question 1 Explanation:
\begin{align} & =\left( 1-\frac{1}{5} \right)\,\left( 1-\frac{1}{6} \right)\,\left( 1-\frac{1}{7} \right)\,......\left( 1-\frac{1}{49} \right)\,\left( 1-\frac{1}{50} \right) \\ & =\left( \frac{5-1}{5} \right)\,\left( \frac{6-1}{6} \right)\,\left( \frac{7-1}{7} \right)\,......\left( \frac{49-1}{49} \right)\,\left( \frac{50-1}{50} \right) \\ & =\frac{4}{5}\times \frac{5}{6}\times \frac{6}{7}\times ......\times \frac{48}{49}\times \frac{49}{50} \\ & =\frac{4}{50} \\ & =\frac{2}{25} \\ \end{align}
 Question 2
$\frac{125{{\left( 1.3 \right)}^{3}}+1}{{{\left( 6.5 \right)}^{2}}-5.5}$ is equal to
 A 2.75 B 9/5 C 4.75 D 7.5
Question 2 Explanation:
\begin{align} & =\frac{125{{\left( 1.3 \right)}^{3}}+1}{{{\left( 6.5 \right)}^{2}}-5.5} \\ & =\frac{{{\left( 5\times 1.3 \right)}^{3}}+1}{{{\left( 6.5 \right)}^{2}}-6.5\times 1+{{1}^{2}}} \\ & =\frac{{{\left( 6.5 \right)}^{3}}+1}{{{\left( 6.5 \right)}^{2}}-6.5\times 1+{{1}^{2}}} \\ & \left[ {{a}^{3}}+{{b}^{3}}=\left( a+b \right)\left( {{a}^{2}}-ab+{{b}^{2}} \right) \right] \\ & =6.5+1 \\ & =7.5 \\ \end{align}
 Question 3
The value of $\frac{{{\left( 1.987-4.523 \right)}^{2}}+{{\left( 1.987+4.523 \right)}^{2}}}{1.987\times 1.987+4.523\times 4.523}$ is
 A 4 B 2 C 2.199 D 3.195
Question 3 Explanation:
Let 1.987=a and 4.523=b
Therefore expression
\begin{align} & =\frac{{{\left( a-b \right)}^{2}}+{{\left( a+b \right)}^{2}}}{{{a}^{2}}+{{b}^{2}}} \\ & =\frac{2\left( {{a}^{2}}+{{b}^{2}} \right)}{{{a}^{2}}+{{b}^{2}}}=2 \\ \end{align}
 Question 4
$\left( 5555\div 110 \right)+\left( 925\div 75 \right)+\left( 5168\div 51 \right)=?$
 A 164.16 B 174.26 C 184.16 D 194.26
Question 4 Explanation:
\begin{align} & ?=\frac{5555}{110}+\frac{925}{75}+\frac{5168}{51} \\ & =50.5+12.33+101.33 \\ & =164.16 \\ \end{align}
 Question 5
$\sqrt{32041}\times \sqrt{1681}-{{\left( 71 \right)}^{2}}={{\left( ? \right)}^{2}}+{{\left( 23 \right)}^{2}}$(? Is approximately equal to)
 A 47 B 42 C 44 D 48
Question 5 Explanation:
\begin{align} & \sqrt{32041}\times \sqrt{1681}-{{\left( 71 \right)}^{2}}={{\left( ? \right)}^{2}}+{{\left( 23 \right)}^{2}} \\ & \Rightarrow 179\times 41-5041={{?}^{2}}+529 \\ & \Rightarrow 2298={{?}^{2}}+529 \\ & \Rightarrow {{?}^{2}}=2298-529=1769 \\ & \Rightarrow ?=\sqrt{1769}=42.06 \\ \end{align}
Approximately equals to 42
Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
There are 5 questions to complete.
 ← List →
 1 2 3 4 5 End

### Want to explore more Arithmetic Tests?

FREE CHEAT SHEET

Learn
How to Master VA-RC

This free (and highly detailed) cheat sheet will give you strategies to help you grow

No thanks, I don't want it.