Solution: (d)

\(\displaystyle ?\approx 21+3.7\times 3\approx 21+11.1\approx 32.1\)

Without pen and paper,

By approximation method, consider 3.7 as 4 and multiply with 3 which gives 12, add 21 we get 33. So the nearest value in options is (d) which is 32.

Solution: (a)

Without pen and per let us try it,

By approximation method, take approximate values of 25.675 as 25 and 1321 as 1300, while 64.328 as 65 and lastly 4001 as 4000.

Now the statement looks like

25% of 1300 + 65% of 4000= ?

25% means 1/4^th value of 1300 which is 325 and 65% of 4000 is 65 multiplied by 40 which is 2600. Add, 325+2600=2925, which is approximately equal to 2912 of our option (a)

Solution: (c)

Approximate cube root of 5826 is 18. Add it to 456 we get RHS as 474. On LHS, consider 31.001 as 30. Multiply it with 474, we get 14220. Since we have decreased 31 to 30, the value we got is little less. So, this is almost in-line with our option (c).

Solution: (d)

Having a glance at the given options one can find out that the two nearest values have a difference of 300. So round off the numbers to the nearest ten’s values.

9228.789 \(\displaystyle \approx \) 9230; 5021.832 \(\displaystyle \approx \) 5020 and 1496.989 \(\displaystyle \approx \) 1500

Now the equation will become

\(\displaystyle 9230-5020+1500=?\)

\(\displaystyle \Rightarrow ?=5710\)

Solution: (d)

The difference between two nearest values is 70 (210 and 280). So round off the numbers to the nearest integers. 29.8% of 260 \(\displaystyle \approx \) 30% of 260; 60.01% of 510 \(\displaystyle \approx \) 60% of 510 and 103.57 \(\displaystyle \approx \) 104

Now by approximation, the equation will become,

\(\displaystyle \frac{{30}}{{100}}\times 260+\frac{{60}}{{100}}\times 510-104=?\)

\(\displaystyle 78+306-104=?\)

\(\displaystyle \Rightarrow ?=384-104=280\)

Solution: (e)

By approximation, the equation will become

68 – 12 – 8 – 1 = ?

?=47

Solution: (d)

By Approximation,

\(\displaystyle ?\approx 118\times 8\times 5\approx 4720\)

Solution: (d)

\(\displaystyle \left[ {39.99\%of(2/5)+60.05\%of(1/5)} \right]\times {{10}^{3}}+?=1\)

By approximation method, take the nearest values

\(\displaystyle \left[ {40\%of(2/5)+60\%of(1/5)} \right]\times 1000+?=1\)

\(\displaystyle \left[ {0.16+0.12} \right]\times 1000+?=1\)

\(\displaystyle ?=1-(0.28)\times 1000\)

\(\displaystyle ?=1-280=-279\)

Without pen and paper,

Taking approximate values and start calculating orally, take the percentages in both aside and divide the 1000, we will be left with only 10. Now on 2/5^th of 40 is 16 and 1/5^th of 60 is 12. So, 12+16 is 28, which when multiplied by 10 is 280. Now subtract this with one, we get – 279.

Solution: (d)

\(\displaystyle {{(17.99)}^{2}}-{{(14.05)}^{2}}+\{(2343.05+81.05)/?\}=229\)

\(\displaystyle {{(18)}^{2}}-{{(14)}^{2}}+\{(2343+81)/?\}=229\)

\(\displaystyle 324-196+\{(2424)/?\}=229\)

\(\displaystyle (2424)/?=101\)

\(\displaystyle ?=24\)

Alternate method in approximation without pen and paper,

Taking approximate values, the equation looks like

\(\displaystyle {{(18)}^{2}}-{{(14)}^{2}}+\{(2343+81)/?\}=229\)

First two numbers look like \(\displaystyle ({{a}^{2}}-{{b}^{2}})\), which is \(\displaystyle (a+b)(a-b)\), So (18+14) (18 – 14) = 32 \(\displaystyle \times \) 4=128, On right hand side we have 229, so on subtracting 229 with 128 we get approximately 100. So, calculating further we get 24.24, approximately 24. On regular practice of mcq on approximation, in the second step only you can guess the answer.   

Solution: (a)

\(\displaystyle {{\left[ {\{(155\div 4)\div 12.96\}} \right]}^{2}}+(1/2)\times (63.03\times 18.02)={{(?)}^{2}}\)

Taking approximate values,

\(\displaystyle {{(?)}^{2}}={{\left[ {\{(156\div 4)\div 13\}} \right]}^{2}}+(1/2)\times (63\times 18)\)

\(\displaystyle {{(?)}^{2}}={{\left[ 3 \right]}^{2}}+(567)\)

\(\displaystyle {{(?)}^{2}}=9+567\)

\(\displaystyle {{(?)}^{2}}=576\)

\(\displaystyle ?=24\)

Alternate method, without pen and paper, oral calculation by using approximation

After taking approximate values, the equation looks like

\(\displaystyle {{\left[ {\{(156\div 4)\div 13\}} \right]}^{2}}+(1/2)\times (63\times 18)={{(?)}^{2}}\)

We consider 155 as 156 since 4 is even number so round off to nearest even number divisible by 4.

156 divided by 4 is 39, which is multiple of 13 so we will be left with 3. Half of 18 is 9 which when multiplied by 63 gives 567. At this stage we can predict the answer from the options as 24, (if students are conversant with squares of important numbers. If not at least if we know the square of 25 which is 625, then also we are near to our answer by approximation method.). So we are good at calculations of mcq of approximation, then it’s a two to three steps process orally. If you are not confident proceed to next step and check.

567+9=576 square root of 576 is 24.