Simplification quiz for practice

1 . Directions (1-5): What will come in place of the question mark (?) in the following questions? $Q.$ $3 \over 19$ of 30% of 3420 = $(?)^2 \times 2$ A). $(81)^2$ B). 7 C). 9 D). 81 Answer & Explanation Answer : Option C   Explanation :   3420 x $30\over 100$ x $3 \over 19$ = $(?)^2$ x 2 $\Rightarrow$ 162 = $(?)^2$ x 2 $\Rightarrow$ $(?)^2$ = $162 \over 2$ = 81 ? = $\sqrt{81}$ = 9 View Answer 2 . 1898 ÷ 73 × 72 = $(?)^ 2$ × 13 A). - 256 B). 256 C). 12 D). 144 Answer & Explanation Answer : Option C   Explanation :   $1898\over 73$ × 72 = $(?)^ 2$ × 13 $\Rightarrow$ 26 x 72 = $(?)^ 2$ × 13 $\Rightarrow$ $(?)^ 2$ = $ 26 \times 72\over 13$ = 144 ? = $\sqrt{144}$ = 12 View Answer 3 . $\sqrt {7^2 \times 24 \times 2 - (11)^3 + 3} = ?$ A). 42 B). 1024 C). 1764 D). 32 Answer & Explanation Answer : Option D   Explanation :   ? = $\sqrt {7^2 \times 24 \times 2 - (11)^3 + 3} $ = $\sqrt{2352 - 1331 + 3}$ = $\sqrt {1024}$ = 32 View Answer 4 . $(0.81)^2 \div (0.729)^3\times(0.9)^2 = (0.9)^{? - 3}$ A). 6 B). 2 C). 4 D). 0 Answer & Explanation Answer : Option D   Explanation :   $(0.81)^2 \div (0.729)^3\times(0.9)^2 = (0.9)^{? - 3}$ $\Rightarrow$$((0.9)^2)^2 \div ((0.9)^3)^3\times(0.9)^2 = (0.9)^{? - 3}$ $\Rightarrow$ $(0.9)^4 \div (0.9)^9\times(0.9)^2 = (0.9)^{? - 3}$ $\Rightarrow$$(0.9)^{4 - 9 + 2} = (0.9)^{? - 3}$ $\Rightarrow$$(0.9)^{-3} = (0.9)^{? - 3}$ $\Rightarrow$$? – 3 = – 3$ $\Rightarrow$$? = 3 – 3 = 0$ View Answer 5 . 65% of $\sqrt{3136} \times 5 = ? + 154$ A). 56 B). 28 C). 35 D). 32 Answer & Explanation Answer : Option B   Explanation :   $65\over100$ x $\sqrt{3136} \times 5 = ? + 154$ $\Rightarrow$ 56 x $65\over100$ x 5 = ? + 154 $\Rightarrow$ 182 = ? + 154 $\Rightarrow$ ? = 182 - 154 = 28 View Answer 6 . Directions (6 - 10): What will come in place of the question mark (?) in the following questions? $Q.$ $(21)^2 - 3717 \div 59 = ? \times 8$ A). 43.75 B). 42.25 C). 45.75 D). 47.25 Answer & Explanation Answer : Option D   Explanation :   $(21)^2 - 3717 \div 59 = ? \times 8$ $\Rightarrow$ 441 - $3717 \over 59$ = ? x 8 $\Rightarrow$ 441 - 63 = ? x 8 $\Rightarrow$ 378 = ? x 8 $\Rightarrow$ ? = $378\over8$ = 47.25 View Answer 7 . 2$1\over 8$ - 1$1\over 16$ = ? + 1$1\over 32$ - 1$9\over 64$ A). 2$9\over 32$ B). 1$9\over 64$ C). 1$11\over 64$ D). None of these Answer & Explanation Answer : Option C   Explanation :   ? = 2 - 1 - 1 + 1 + $[$ $1\over 8$ - $1\over 16$ - $1\over 32$ + $ 9\over 64$ $]$ = 1 + $ 8 - 4 - 2 + 9 \over 64 $ = 1 + $11 \over 64$ = 1$11\over 64$ View Answer 8 . $(0.64)^4\div(0.512)^3\times(0.8)^4 = (0.8)^{? + 3}$ A). 5 B). 12 C). 0 D). 6 Answer & Explanation Answer : Option C   Explanation :   $(0.64)^4\div(0.512)^3\times(0.8)^4 = (0.8)^{? + 3}$ $\Rightarrow$ $((0.8)^2)^4\div((0.8)^3)^3\times(0.8)^4 = (0.8)^{? + 3}$ $\Rightarrow$ $(0.8)^8\div(0.8)^9\times(0.8)^4 = (0.8)^{? + 3}$ $\Rightarrow$ $(0.8)^{8 - 9 + 4} = (0.8)^{? + 3}$ $\Rightarrow$ $(0.8)^{3} = (0.8)^{? + 3}$ $\Rightarrow$ ? + 3 = 3 $\Rightarrow$ ? = 0 View Answer 9 . 34.5% of 1800 + 12.4% of 1500 = $(?)^ 3$ + 78 A). 27 B). 9 C). 81 D). 162 Answer & Explanation Answer : Option B   Explanation :   $1800 \times 34.5 \over 100$ + $1500 \times 12.4 \over 100$ = $(?)^3$ + 78 $\Rightarrow$ 621 + 186 = ?$^3$ + 78 $\Rightarrow$ ?$^3$ = 807 - 78 = 729 = 9$^3$ $\Rightarrow$ ? = 9 View Answer 10 . $\sqrt {15^2 \times 12 \div (9) - 125 + 21}$ = ? A). 18 B). 24 C). 196 D). 14 Answer & Explanation Answer : Option D   Explanation :   ? = $\sqrt {225 \times 12 \over 9} - 125 + 21$ = $\sqrt {300 - 125 + 21 }$ = $\sqrt {196}$ = 14 View Answer