Simplification for IBPS PO test 6-Solved questions with detailed explanations for SSC, IBPS PO, SBI PO, RRB, RBI, CSE, CGL, CHSL, CDA, CSE, UPSC

1)

What will come in place of question mark (?) in the following questions

img/Type5-Q126

[lOB (PO), 2010]

A)
5
B)
4
C)
7
D)
6
E)
None of these

Answer: Option E

Explanation

$\begin{array}{l} Here, applying the rules of surds and \\ indices, we get \\ {(9)}^{3/2} \times {(9)}^{5/2} \div {(27)}^{2} {= (3)}^{?} \\ \Rightarrow {(3)}^{2 \times 3/2} \times {(3)}^{2 \times 5/2} \div {(3^{3})}^{\times 2} {= (3)}^{?} \\ \Rightarrow 3^{3+ 5 - 6} {= (3)}^{?} \\ \Rightarrow ? = 2 \end{array}$

Hence Option E is correct.

Discussion

2)

$\frac{16 \times 32}{9 \times 27 \times 81} = ?$

[Corporation Bank (PO), 2009]

A)
${(\frac{2}{3})}^{12}$
B)
${(\frac{2}{3})}^{11}$
C)
${(\frac{2}{3})}^{13}$
D)
${(\frac{2}{3})}^{9}$
E)
None of these

Answer: Option D

Explanation

$\begin{array}{l} Here, \frac{2^{4} \times 2^{5}}{3^{2} \times 3^{3} \times 3^{4}} \\ [\begin{array}{l} ∵ 16 = 2^{4}, 32 = 2^{5} \\ 9 = 3^{2}, 27 = 3^{3} \\ 81 = 3^{4} \end{array}] \\ By applying the rule of indices, \\ = \frac{2^{9}}{3^{9}} = {(\frac{2}{3})}^{9} \end{array}$

Hence, Option D is correct.

Discussion

3)

${(49)}^{3} \div {(7)}^{2} = ?$

[New India Insurance (PO), 2009]

A)
2401
B)
49
C)
343
D)
7
E)
None of these

Answer: Option A

Explanation

Here,

$= {(7^{2})}^{3} \div {(7)}^{2} = ? = {(7)}^{6} \div {(7)}^{2} = ? = 7^{6 - 2} = ? [∴ 7^{6} \div 7^{6 - 2}] = ? = 7^{4} = 7 \times 7 \times 7 \times 7 = 2401$

Hence, option A is correct.

Discussion

4)

$64^{3.1} \times 8^{4.3} = 8^{?}$

[Corporation Bank (PO), 2009]

A)
10.5
B)
7.4
C)
1.2
D)
13.3
E)
None of these

Answer: Option A

Explanation

$\begin{array}{l} {Here, (64)}^{3.1} \times 8^{4.3} = 8^{?} \\ By applying the rule of indices, we get \\ = (8^{2})^{3.1} \times {(8)}^{4.3} {= 8}^{?} \\ = 8^{?} {= 8}^{6.2+4.3} \\ {= 8}^{10.5} \\ \Rightarrow ? = 10 .5 \end{array}$

Hence, Option A is correct.

Discussion

5)

$8^{7} \times 2^{6} \div 8^{2.4} {= 8}^{?}$

[OBC (PO), 2009]

A)
10.6
B)
9.6
C)
8.6
D)
6.6
E)
None of these

Answer: Option D

Explanation

$\begin{array}{l} {Here, 8}^{7} \times {(2^{3})}^{2} \div 8^{24} {= 8}^{?} \\ Applying the rule of indices, we get \\ 8^{7} \times 8^{2} \div 8^{2.4} {= 8}^{?} \\ \Rightarrow 8^{7+2 - 2.4} {=8}^{?} \\ \Rightarrow 8^{?} {= 8}^{9-2.4} {= 8}^{6.6} \\ \Rightarrow ? = 6.6 \end{array}$

Hence, Option D is correct.

Discussion

Simplification-Test 6 (Based on Surds and Indices/Percentages)

Answer: Option E

Answer: Option D

Answer: Option A

Answer: Option A

Answer: Option D