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Joined: 02 Jan 2020
Status:GRE Quant Tutor
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Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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Factors and Multiples Question Set (Easy-Medium)
[#permalink]
22 Apr 2023, 20:30
22 Apr 2023, 20:30
Show: :: DOWNLOAD PDF: Factors and Multiples Question Set (Easy-Medium)
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Factors and Multiples Question Set (Easy-Medium)
Attached pdf of this Article as SPOILER at the top! Happy learning!
Hi All,
I have recently uploaded a video on YouTube to discuss Factors and Multiples Question Set (Easy-Medium) in Detail:
Six solved problems are covered in the video.
Q1. If 26 is a factor of n, then is 6 a factor of n?
Show: ::
Sol: 26 is a factor of n => n is a multiple of 26
=> n = 26k where k is an integer
For 6 to be a factor of n, 26k should be divisible by 6
We need a 2 and a 3 for 6, but we have only 2 in 26k (=2 * 13k)
So, 26k will be divisible by 6 only when k is divisible by 3, which might not be true always
=> We CANNOT say for sure if 6 is a factor of n.
=> n = 26k where k is an integer
For 6 to be a factor of n, 26k should be divisible by 6
We need a 2 and a 3 for 6, but we have only 2 in 26k (=2 * 13k)
So, 26k will be divisible by 6 only when k is divisible by 3, which might not be true always
=> We CANNOT say for sure if 6 is a factor of n.
Q2. If 90 is a factor of n, then is 20 a factor of n?
Show: ::
Sol: 90 is a factor of n => n is a multiple of 90
=> n = 90k where k is an integer
For 20 to be a factor of n, 90k should be divisible by 6
We need a 2 and a 10 for 20, but we have only 10 in 90k (=10 * 9k)
So, 90k will be divisible by 20 only when k is divisible by 2, which might not be true always
=> We CANNOT say for sure if 20 is a factor of n.
=> n = 90k where k is an integer
For 20 to be a factor of n, 90k should be divisible by 6
We need a 2 and a 10 for 20, but we have only 10 in 90k (=10 * 9k)
So, 90k will be divisible by 20 only when k is divisible by 2, which might not be true always
=> We CANNOT say for sure if 20 is a factor of n.
Q3. If 24 is a factor of n, then is n a multiple of 8?
Show: ::
Sol: 24 is a factor of n => n is a multiple of 24
=> n = 24k where k is an integer
n = 24k = 8 * 3k
=> Clearly, n is a multiple of 8 => TRUE.
=> n = 24k where k is an integer
n = 24k = 8 * 3k
=> Clearly, n is a multiple of 8 => TRUE.
Q4. If 4 and 6 are factors of x, then which of the following will be a factor of x for sure
A. 8
B. 12
C. 24
D. 36
E. 48
Show: ::
Sol: 4 and 6 are factors of n => n is a multiple of LCM(4,6)
=> n = LCM(4,6) * k where k is an integer
= 12k
=> n is a multiple of 12 for sure
=> So, Answer will be D.
=> n = LCM(4,6) * k where k is an integer
= 12k
=> n is a multiple of 12 for sure
=> So, Answer will be D.
Q5. If 12 is a factor of x and 16 is a factor of y, then
5.1 Is 48 a factor of xy?
5.2 Is 96 a factor of xy?
5.3 Is 192 a factor of xy?
Show: ::
Sol: 12 is a factor of x
=> x is a multiple of 12 => x = 12a
16 is a factor of y
=> y is a multiple of 16 => y = 16b
xy = 12a * 16b = 192 ab
So, xy is a multiple of
48 because xy = 48*4*ab
96 because xy = 96*2 *ab
192 because xy= 192*1*ab
So, Answer will be TRUE for all three problems
=> x is a multiple of 12 => x = 12a
16 is a factor of y
=> y is a multiple of 16 => y = 16b
xy = 12a * 16b = 192 ab
So, xy is a multiple of
48 because xy = 48*4*ab
96 because xy = 96*2 *ab
192 because xy= 192*1*ab
So, Answer will be TRUE for all three problems
Q6. In a competition, gold medal gives 7 points, Silver gives 5 points and bronze gives 3 points. Roger participated in the competition in various events and the product of all the points earned by him is 33075. Then find the number of gold, silver and bronze medal earned by Roger
Show: ::
Sol: Bronze = x, Silver = y, Gold = z
Product of all the points = 33075
=> 33075 = \(3^x * 5^y * 7^z\)
33075 = \(3^3 * 5^2 * 7^2\)
\(3^3 * 5^2 * 7^2\) = \(3^x * 5^y * 7^z\)
So, Answer will Roger won: Gold – 2, Silver – 2, Bronze - 3
Product of all the points = 33075
=> 33075 = \(3^x * 5^y * 7^z\)
33075 = \(3^3 * 5^2 * 7^2\)
\(3^3 * 5^2 * 7^2\) = \(3^x * 5^y * 7^z\)
So, Answer will Roger won: Gold – 2, Silver – 2, Bronze - 3
Watch the following video to learn the Basics of Factors and Multiples
Hope it helps!
Good Luck!
gmatclubot
Factors and Multiples Question Set (Easy-Medium) [#permalink]
22 Apr 2023, 20:30
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