Data Sufficiency

If 1/4 of the larger of two numbers is greater than 5 times the smaller of the same two numbers, is the smaller number less than 4?

1) The larger number is greater than 70
2) The larger number is less than 80

[spoiler]Answer: B[/spoiler]

a,b. and a>b
a/4 > 5b or a>20b... b<4???
A) a>70. if a=80,b<4 and if a=120, b<6. insufficient
B) a<80 or 20b<a<80 or b<4
IMO B

Let l be the larger number and s be the smaller number
Given that l/4>5s or l>20s i.e. the larger number is greater than 20 times the smaller number so is s<4?

(1)Lets assume l=71 so we have 71>20s or 71/20>s re written as s<3.5 so YES. Now lets take l=85
so we have 85/20>s rewritten as s<4.25 so s could be greater than 4. Since we get conflicting answers this statement is insufficient

(2)Let the number be 79 so we have 79>20s or 79/20>s rewritten as s<3.95
Let l=25 so we have 25>20s or 1.25>s .You can try plugging in different values for l<80 in this inequality and you'll see that s is always less than 4 . This statement is sufficient. Hence B

I prefer to approach questions like this by fleshing out the prompt before reading the statements.

We are told (1/4)x > 5y, or x/20 > y
We are asked if y < 4.
Since we know y < x/20, then y < 4 will be true if x/20 <= 4, or x <= 80.

Once we know that we can go through the statements and answer the question pretty quickly.

When looking at a DS question it is often best to identify the content area and work with the original statements before looking at the numbered statements. Here is says that 1/4 of a larger number is greater than 5 times a smaller number - this is all algebra so it would be a good idea to set up the equation:

1/4(L)>5S now you can manipulate that to get the S on one side so you get 1/20(L)>S. Then incorporate the question which is S<4? If S is less than 4 then L would be less than 80 so that is the real question being asked - is L less than 80?

Statement 1 says L is greater than 70 which includes both numbers less than and greater than 80. So it is insufficient.

Statemetn 2 says that L is less than 80 which is the exact information we are looking for - and the answer is B.