0 1/10

Question

0 1/10

Fijisurf · Answer

D

(1) Lets pick numbers (a<10): if a=1/3 , then b=1/2 to make the formula work.
if a>10, for example a=15, then b has to be 15/29 (because 1/a +1/b =5 is the same as: a+b=5ab). However, we know that b>a therefore ahas to be less than 10. Sufficient.

(2) 1/a>1/10 => 10>a - Sufficient

afyl128 · Answer

How do you manipulate 1/a>1/10 to 10>a

is there an intermediate step?

Fijisurf · Answer

I find the expression 1/a +1/b =5 kind of tricky.

You can transform it to (a+b)=5ab, which is a=b(5a-1) which is b=a/(5a-1)

Now by trying different a's you can see what b becomes.

If 0<a<1, then b <1. (a=1/3; b=1/2)
If a>1, then still b<1, (a=2, b=2/9 or a=15, b=15/74) which contradicts to the question stem, that "a" has to be less than "b".

shrouded1 · Answer

I find the expression 1/a +1/b =5 kind of tricky.

You can transform it to (a+b)=5ab, which is a=b(5a-1) which is b=a/(5a-1)

Now by trying different a's you can see what b becomes.

If 01, then still b1, you get that b is always <1, which just means that no such solution is possible. Which means given the constraint and given the statement a is always less than 1, which is why it is sufficient to say a<10

0<a<b is a<10? 1. 1/a +1/b =5 2. 1/a > 1/10

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