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Quantitative Reasoning – Fill in the blanks using mathematical operators!

2014_QNR 22. If you have to use all the four mathematical operations (+, —, ×, ÷) only once in the blanks below, what is the maximum number you get if at no stage you have a fraction or a negative number ?
3 ___8 ___2 ___5 ___8 = ?
(a) 9

(b) 8

(c) 18

(d) 15

Ans: Although this is more or less trial and error, let us understand that we should not try putting ‘÷‘ in first, second or last blank [we do not want fraction at any stage and BODMAS rule gives higher precedence to ÷]. Let us put ÷ in the second blank to minimize our attempts to find the maximum number:

3 ___8 ÷ 2 ___5 ___8 

The expression now becomes “3 ___4 ___5 ___8 “.

Now, the minus operator (-) should not be put between 3 and 4; we will end up getting negative number because rest of the two places will be occupied by ‘+’ and ‘x’. Since we want to maximize the number, let us try putting in ‘x’ in the first place:

“3 X 4  + 5  – 8” => 9. We can also interchange the ‘+’ and ‘-‘ symbols.

“3 X 4  – 5  + 8” => 15.

Two more possible combinations remain where between ‘3’ and ‘4’ we put ‘+’.

“3 + 4  X 5  – 8” => 15 and  “3 + 4  – 5  x 8” => -ve.

Thus, the maximum possible value=15. Option d.

 

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