Which one of the following is closest to 1?

Question

A.  \frac{3}{3+0.3}

B.  \frac{3}{3+0.3^2}

C.  \frac{3}{3-0.3}

D.  \frac{3}{3-0.3^2}

E.  \frac{3}{3+0.33}

KSBGC · Answer

If we have same numerator and denominator we will get 1 after division .

Option B.

observe . we have 3 + 0.3 as common base in all options.

but in B , denominator is a slightly more than 3.

The best option is B.

LevanKhukhunashvili · Answer

At first, I was confused, as B and D are very similar.
In B, 3 is increased by 0.09 and in D 3 is decreased by 0.09.
As I didn't know any rule to solve my dilemma, I just picked some more convenient numbers to deal with
5/5=1; 
5/4=1.25 --> 0.25 more than 1
5/6=~0.83 --> 0.17 Less than 1

So dealing with slightly big denominator is favorable in our case

IMO
Ans:  B

smita123 · Answer

Please explain why E is wrong and B is right.

0.3^2 will be 0.09 which is less than 0.33. We need a big denominator so the answer should be E.

shalavkalaan · Answer

Question is incorrect. E is answer. Only in case E has 3^3 B can be answer.

Posted from my mobile device

m1033512 · Answer

Here for B I get .96 approx

and for D I get 1.03 approx

so D should be correct as it is .03 away from 1 while B is .04 points away from 1

so closet to 1 should be option D

Please correct me where I get this wrong

Posted from my mobile device

jackfr2 · Answer

for B it's .971 approx and 
for D it's 1.031 approx.

so calculate distance to 1 and you'll get the answer is B.

chetan2u · Answer

Which one of the following is closest to 1?

First discard the values by comparing
(1) If the value is <1, then keep the largest of these.
All terms with the denominators 3+xy will be <1. Largest will be the term with smallest denominator as the numerators are the same.
Here, amongst \(3+0.3,3+0.3^2,3+0.33\), the smallest is 3+0.3^2, so keep B and discard A and E.
(2) If the value is >1, then keep the smallest of these.
All the terms with denominators 3-xy will be >1. Smallest will be the term with largest denominator as the numerators are the same.
Here, between \(3-0.3,3-0.3^2,\), the larger is 3-0.3^2, so keep D and discard C.

Simplify and then subtract 1. The smallest value after discarding the SIGN is the answer.

B. \(\frac{3}{3+0.3^2}\)
\(\frac{3}{3+0.3^2}-1\)
=>\(\frac{-0.09}{3.09}\)

D. \(\frac{3}{3-0.3^2}\)
\(\frac{3}{3-0.3^2}-1\)
=>\(\frac{+0.09}{2.91}\)

The results are nothing but distance from 1
As the numerators are the same, the smallest will be the term with largest denominator.
B is the answer.

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Which one of the following is closest to 1?

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Which one of the following is closest to 1?

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