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tens digit of (Z - 91) is 3

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tens digit of (Z - 91) is 3

by arora007 » Tue Jul 06, 2010 8:20 am
If Z is a three-digit positive integer, what is the value of the tens digit of Z ?

1. The tens digit of (Z - 91) is 3
2. The units digit of (Z + 9) is 5

OA is C

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by albatross86 » Tue Jul 06, 2010 8:37 am
Z is a 3-digit positive integer. What is the tens digit of Z?

1. Tens digit of Z - 91 = 3

Let's say Z - 91 = 130 => Z = 221
Z - 91 = 239 => Z = 330

Ten's digit is different in both cases.
INSUFFICIENT

2. Units digit of Z + 9 = 5

Let's say Z + 9 = 135 => Z = 126
Z + 9 = 145 => Z = 136

Ten's digit is different in both cases.
INSUFFICIENT

Both 1 and 2 together:

Now from 2, we saw that the units digit of Z must be 6. (In order that Z + 9 has units digit 5)

Z - 91 has ten's digit 3. In order to get units digit of Z as 6, (Z - 91) must have units digit of 5, so that when 91 is added you get the 6 you need.

egs: Z - 91 = 235 => Z = 326
Z - 91 = 435 => Z = 526

i.e. The units digit MUST be 6 and thus the ten's digit of Z MUST be 2 to satisfy statement 1.

SUFFICIENT

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