Bowl X has 4 cards in it, numbered 1 - 4. Bowl Y has 5 cards in it, numbered 5 - 9. What is the probability that the sum of a card pulled randomly from Bowl X and a card pulled randomly from Bowl Y will equal 8?

A. 1/20
B. 1/10
C. 3/20
D. 2/16
E. 3/16
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

NOTE: In order to get a sum of 8, the card selected from Bowl X must be 1, 2 or 3.
Here's why: Cards 1, 2 and 3 all have corresponding cards in Bowl Y that add to get 8 (i.e., 1+7 = 8, 2+6 = 8 and 3+5 = 8)
However, card 4 (from Bowl X) does NOT have a corresponding card in Bowl Y that add to get 8.

So P(sum is 8) = P(card selected from Bowl X is 1, 2 or 3 AND card selected from Bowl Y is the one card that works with the first card to get a sum of 8)
= P(card selected from Bowl X is 1, 2 or 3) x P(card selected from Bowl Y is the one card that works with the first card to get a sum of 8)
= 3/4 x 1/5
= 3/20

Answer: C

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com