vinnik wrote:

If ab = ac is b = 2 ?

(1) c = 1

(2) a is a prime number and c is NOT a prime number

I got this step correct \(a(b-c)=0\) : either \(a=0\) or \(b=c\)

But (1), i selected this one as the answer along with (2)

Not sure why this isn't correct. My understanding says b = 1 because b = c, which is 1.

Not able to understand (1)'s explanation:- \(c=1\) . If \(a=0\) then \(b\) can take any value irrespective of the value of \(c\) . Not sufficient.

Please explain this in detail.

Thanks & Regards

Vinni

OFFICIAL SOLUTION:

If \(ab=ac\) is \(b=2\)?

Notice that we cannot reduce \(ab=ac\) by \(a\) and write \(b=c\), since \(a\) can be zero and division by zero is not allowed. \(ab=ac\) --> \(a(b-c)=0\) --> either \(a=0\) or \(b=c\).

(1) \(c=1\) --> if \(a=0\) then \(b\) can tale any value irrespective of the value of \(c\). Not sufficient.

(2) \(a\) is a prime number and \(c\) is NOT a prime number --> \(a=prime\) means that \(a\neq{0}\), so it must be true that \(b=c\). Now, since also given that \(c\neq{prime}\) then \(b\) is also not equal to a prime number so it cannot equal to a prime number 2. Sufficient.

Answer: B.

As for your question. We have that either a=0

OR b=c.

Now, if for (1) a=0, then b can take ANY value. Consider a=0, c=1 and b=(any value) --> ab=ac=0.

Hope it's clear.

_________________

New to the Math Forum?

Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:

GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

Extra-hard Quant Tests with Brilliant Analytics