Question : Which smallest positive number should be subtracted from each of 9 and 13 so that 18 is the third proportion to them?
Option 1: 2
Option 2: 4
Option 3: 3
Option 4: 1
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Correct Answer: 1
Solution : Let the required number be $x$. For third proportional of $9-x$ and $13-x$, $(9-x):(13-x)::(13-x):18$ So, $\frac{(9-x)}{(13-x)}=\frac{(13-x)}{18}$ ⇒ $18\times (9-x)=(13-x)^2$ ⇒ $162-18x=169-26x+x^2$ ⇒ $x^2-8x+7=0$ ⇒ $(x-1)(x-7)=0$ ⇒ $x=1,2$ Since we need the smallest number, $x=1$ Hence, the correct answer is 1.
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Question : What smallest positive number should be subtracted from 2 and 3 so that 4 is the third proportion to them?
Option 1: 1
Option 2: 2
Option 3: 4
Option 4: 3
Question : The least number that must be subtracted from 1294 such that the obtained number when divided by 9, 11, and 13, leaves in each case the same remainder of 6, is:
Option 2: 3
Option 3: 1
Option 4: 4
Question : Find the smallest number that can be subtracted from 148109326 so that it becomes divisible by 8.
Option 1: 4
Option 2: 8
Option 3: 6
Option 4: 10
Question : Which of the following is the smallest ratio? $\frac{5}{6}, \frac{7}{9}, \frac{11}{12}, \frac{13}{18}$
Option 1: $\frac{7}{9}$
Option 2: $\frac{13}{18}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{11}{12}$
Question : What should be subtracted from 246837 to make it divisible by 13?
Option 2: 5
Option 4: 6
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