DS - Hundredths & Tenths

[karthikpandian19]

Y and Z are both positive numbers less than 1. Is Y > Z ?

1. The hundredths digit of Y is greater than the tenths digit of Z and less than the hundredths digit of Z.
2. The thousandths digit of Y is greater than the hundredths digit of Y and less than the tenths digit of Y.

[eagleeye]

Hi karthikpandian19:

The correct answer should be C. Let me explain:

We are given that Y and Z are positive numbers less than 1, so 0<Y<1, and 0<Z<1.
We need to find whether Y>Z. Note that since Y and Z are decimals less than one, if we can determine whose "tenths" digit is larger, we have a sufficient condition.

1. The hundredths digit of Y is greater than the tenths digit of Z and less than the hundredths digit of Z.
Let Y = 0.abc where a,b,c are non-negative integers (and we know that Y<1)
and Z = 0.def where d,e,f are non-negative integers (and we know that Z<1)

Then we have "hundredths digit of Y is greater than the tenths digit of Z and less than the hundredths digit of Z." which means that b>d and b<e. (d<b<e)
This doesn't tell us anything about the tenths digit of Y, hence INSUFFICIENT.
For argument's sake, let's look at two examples where (d<b<e condition is satisfied).

If Y=0.227, and Z=0.139, Z<Y
If Y=0.127, and Z=0.139, Z>Y.
So, still INSUFFICIENT

Let's look at statement 2:

2. The thousandths digit of Y is greater than the hundredths digit of Y and less than the tenths digit of Y.
This tells us that for Y=0.abc, c>b, and c<a. which is b<c<a. This doesn't tell us anything about Z. INSUFFICIENT.

Let's consider the two together.
From the first we have d<b<e, from the second we have b<c<a,
So we know d<b and b<a, hence d<a. This means that the "tenths" digit of Z is smaller than that of Y. This is what we were looking for. Hence Z<Y. SUFFICIENT. Hence the answer is C.

Let me know if this helps

[ronnie1985]

(C)

QQED