Solution: (b)
\(\displaystyle ?\approx \sqrt{{8000}}\approx 89\)
We can orally do it by, approximation, 90 multiplied two time is 8100. Our answer is just 100 short of the 8000, so the answer is 89.
22) \(\displaystyle 99999\div 99\div 9=?\)
(a) 112
(b) 211
(c) 121
(d) 221
(e) 222
Solution: (a)
\(\displaystyle ?=\frac{{99999}}{{99\times 9}}\approx 112\)
Without pen and paper,
Assume all numbers near to their respective nearest tens, hundreds and thousands and start dividing, we will get 100 as answer. So, by approximation our answer should be very near to 100. We see that out of the given options 112 is the least number near to 100. If you get a doubt that it may be option (c) i:e 121. We can check that, like 100000 divided by 100 is 1000, which if again divided by 9 we get 111.11. So by approximation method the answer is (a) only.
Solution: (c)
Let x be there in place of question mark so, \(\displaystyle x\%of45.999\times 16\%of83.006=116.073\)
We take \(\displaystyle \frac{x}{{100}}\times 46\times \frac{{16}}{{100}}\times 89=116\)
By approximation,
\(\displaystyle \frac{x}{{100}}\times 50\times \frac{{16}}{{100}}\times 83=116\)
\(\displaystyle x\times 0.5\times 1.28=116\)
\(\displaystyle x\times 6=116\) (approx)
\(\displaystyle \Rightarrow x=19.33\approx 19\)
29) 9228.789 – 5021.832 + 1496.989 = ?
(a) 6500
(b) 6000
(c) 6300
(d) 5700
(e) 5100
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.
\(\displaystyle 9228.789\approx 9230;\text{ }5021.832\approx 5020\text{ }and\text{ }1496.989\approx 1500\)
Now the equation will become
9230 – 5020 + 1500 = ?
? = 5710
Solution: (a)
It can be rounded off to the nearest ten’s places.
\(\displaystyle 1002\approx 1000;\text{ }49\approx 50;\text{ }99\approx 100\text{ }and\text{ }1299\approx 1300\)
Now the equation will become
\(\displaystyle 1000\div 50\times 100-1300=?\)
\(\displaystyle 20\times 100-1300=?\)
2000 – 1300 = ?
? = 700
