## Hard algebra questions for SSC CGL Set 74: Use algebra problem solving techniques

The 10 hard algebra questions with answers for SSC CGL math test will greatly benefit your practice and proficiency in solving tough algebra questions.

The questions we have selected are from actual previous SSC CGL exams, ensuring maximum impact in a short time.

The practice will also prepare you for SSC CHSL, SSC CPO, and other competitive exams, while establishing a strong foundation for the SSC CGL Tier II exam.

Verify answers and then read solutions in the link at the end to know how to answer the tough questions quickly and correctly in time.

*Set the timer ON and take the test now in all seriousness. And after the test, make sure you don’t miss our valuable TIPs on quick answering objective hard algebra questions quickly and confidently*.

### 16th set of 10 tough algebra questions for SSC CGL Math 74 - answering time 12 mins

**Q1. **If $a:b=2:3$ and $b:c=4:5$, find $a^2:b^2:bc$.

- $16:36:20$
- $4:9:45$
- $4:36:40$
- $16:36:45$

**Q2.** If $a+b+c=4\sqrt{3}$ and $a^2+b^2+c^2=16$, then the ratio of $a:b:c$ is,

- $1:\sqrt{2}:\sqrt{3}$
- $1:2:3$
- $1:1:1$
- None of these

**Q3. **If $x^2+y^2+z^2=2(x+z-1)$, then the value of $x^3+y^3+z^3$ is,

- $0$
- $1$
- $2$
- $-1$

**Q4. **If $a+b+c=0$, then the value of $2b^2c^2+2c^2a^2+2a^2b^2 - a^4-b^4-c^4$ is,

- 7
- 0
- 28
- 14

**Q5. **If $\displaystyle\frac{a}{b}=\frac{2}{3}$ and $\displaystyle\frac{b}{c}=\frac{4}{5}$ then the value of the ratio $\displaystyle\frac{a+b}{b+c}$ is,

- $\displaystyle\frac{20}{27}$
- $\displaystyle\frac{8}{6}$
- $\displaystyle\frac{6}{8}$
- $\displaystyle\frac{27}{20}$

**Q6.** If $U_n=\displaystyle\frac{1}{n}-\displaystyle\frac{1}{n+1}$, then the value of $U_1+U_2+U_3+U_4+U_5$ is,

- $\displaystyle\frac{1}{2}$
- $\displaystyle\frac{1}{3}$
- $\displaystyle\frac{5}{6}$
- $\displaystyle\frac{2}{5}$

** Q7.** If $a*b=2a+3b-ab$, then the value of $(3*5+5*3)$ is,

- 2
- 4
- 6
- 10

** Q8.** If $\displaystyle\frac{x}{2x^2+5x+2}=\frac{1}{6}$, then the value of $x+\displaystyle\frac{1}{x}$ is,

- $2$
- $-2$
- $-\displaystyle\frac{1}{2}$
- $\displaystyle\frac{1}{2}$

**Q9.** If $x=\displaystyle\frac{\sqrt{3}+1}{\sqrt{3}-1}$, and $y=\displaystyle\frac{\sqrt{3}-1}{\sqrt{3}+1}$, then the value of $x^2+y^2$ is,

- $13$
- $0$
- $14$
- $15$

** Q10.** If $\displaystyle\frac{2x-y}{x+2y}=\displaystyle\frac{1}{2}$, then the value of $\displaystyle\frac{3x-y}{3x+y}$ is,

- $1$
- $\displaystyle\frac{3}{5}$
- $\displaystyle\frac{1}{5}$
- $\displaystyle\frac{4}{5}$

### Answers to the hard algebra questions for SSC CGL Set 74

**Problem 1.** Answer: Option d: $16:36:45$.

**Problem 2.** Answer: Option c : $1:1:1$.

**Problem 3.** Answer: Option c: 2.

**Problem 4.** Answer: Option b: 0.

**Problem 5.** Answer: Option a: $\displaystyle\frac{20}{27}$.

**Problem 6.** Answer: Option c : $\displaystyle\frac{5}{6}$.

**Problem 7.** Answer: Option d: 10.

**Problem 8.** Answer: Option d: $\displaystyle\frac{1}{2}$.

**Problem 9.** Answer: Option c: $14$.

**Problem 10.** Answer: Option b: $\displaystyle\frac{3}{5}$.

It’s alright if you don’t finish answering all 10 hard SSC CGL Algebra questions correctly in time. Repeated practice and pattern-based techniques will help you achieve the perfect score in 12 minutes or less.

Read on to learn how you can do it.

### How to solve the questions quickly and correctly

To know how to solve the questions quickly, read the solutions at,

* SSC CGL level Solution Set 74, Algebra 16*.

And go through the extensive * Quick Algebra selected question solutions* to build a strong foundation on

**how to use ALL pattern-based special algebra problem solving techniques.**Use these tips to further improve your skills.

### TIPS for QUICK ANSWERING Objective Hard Algebra Questions

From years of experience in solving SSC CGL algebra questions quickly, the short list of tips for accurate and quick answering of difficult algebra questions are compiled.

You,

1. Must have a good understanding of the

BASIC CONCEPTSof the topic.

2. Are ADEQUATELY fast in mental math calculation: For SSC CGL math, lightning fast mental calculation NOT NEEDED at all.

3. Should FORGET USING TRICKS. Instead, first use basic concepts and then advanced concepts created from basic concepts. Identifying key patterns in a problem is vital for quick solution.

4. DO NOT MEMORIZE formulas. Practice solving many SELECTED problems, if needed REPEATEDLY, to know by heart

how to identify the key patternsin the problem andtake the action for solving the problem quick and correct.

5. WRITE DOWN the most used concepts and formulas for solving algebra MCQs in two sheets of paper (try to be short because it is for yourself). This writing down will help in recall when you need. You will get PRACTICALLY ALL FORMULAS AND TECHNIQUES NEEDED FOR SOLVING ALGEBRA MCQS IN SSC CGL in Suresolv. Go through the articles at your pace using the links in

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6. DO MOST of the REASONING IN YOUR HEAD without touching pen on paper. Make it a habit during practice sessions. If needed repeat a test of 10 algebra mcqs.

7. Go through the most used algebra problem solving FORMULAS AND TECHNIQUES in

Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems.

### Guided help on Algebra in Suresolv

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