Stiv wrote:
If k, m, and t are positive integers and \frac {k}{6} + \frac {m}{4} = \frac {t}{12} , do t and 12 have a common factor greater than 1?
(1) k is a multiple of 3.
(2) m is a multiple of 3.
In the explanation of this question they say that the sum of two multiples of 3 give the number that is also a multiple of 3.
Is that a general rule for any number? If someone can elaborate I would be grateful!
If k, m, and t are positive integers and \frac{k}{6} + \frac{m}{4} = \frac{t}{12}, do t and 12 have a common factor greater than 1 ?\frac{k}{6} + \frac{m}{4} = \frac{t}{12} -->
2k+3m=t.
(1) k is a multiple of 3 -->
k=3x, where
x is a positive integer -->
2k+3m=6x+3m=3(2x+m)=t -->
t is multiple of 3, hence
t and 12 have a common factor of 3>1. Sufficient.
(2) m is a multiple of 3 -->
m=3y, where
y is a positive integer -->
2k+3m=2k+9y=t -->
t and 12 may or may not have a common factor greater than 1. Not sufficient.
Answer: A.
As for your question:
If integers a and b are both multiples of some integer k>1 (divisible by k), then their sum and difference will also be a multiple of k (divisible by k):Example:
a=6 and
b=9, both divisible by 3 --->
a+b=15 and
a-b=-3, again both divisible by 3.
If out of integers a and b one is a multiple of some integer k>1 and another is not, then their sum and difference will NOT be a multiple of k (divisible by k):Example:
a=6, divisible by 3 and
b=5, not divisible by 3 --->
a+b=11 and
a-b=1, neither is divisible by 3.
If integers a and b both are NOT multiples of some integer k>1 (divisible by k), then their sum and difference may or may not be a multiple of k (divisible by k):Example:
a=5 and
b=4, neither is divisible by 3 --->
a+b=9, is divisible by 3 and
a-b=1, is not divisible by 3;
OR:
a=6 and
b=3, neither is divisible by 5 --->
a+b=9 and
a-b=3, neither is divisible by 5;
OR:
a=2 and
b=2, neither is divisible by 4 --->
a+b=4 and
a-b=0, both are divisible by 4.
Hope it's clear.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
close
52% (02:47) correct
