have the same prime factors

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

have the same prime factors

by sanju09 » Tue Mar 16, 2010 5:55 am

Two different numbers have the same prime factors, but one of the numbers has two more factors than the other. Which of the following would correctly represent the two numbers?
(A) 20 & 60
(B) 20 & 80
(C) 30 & 60
(D) 40 & 80
(E) 50 & 100

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Problem Solving | Tue Mar 16, 2010 5:55 am

kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 am; Thanked: 47 times; Followed by:2 members

by kstv » Tue Mar 16, 2010 6:04 am

All the numbers are in 10s so divisible by 5 (prime no) and 2 . Divide by 10
A) 20 & 60 2 6
(B) 20 & 80 2 8
(C) 30 & 60 3 6
(D) 40 & 80 4 8
(E) 50 & 100 5 10
Only 8 is 2Â³ two more factos then 2

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Tue Mar 16, 2010 6:18 am

kstv wrote:All the numbers are in 10s so divisible by 5 (prime no) and 2 . Divide by 10
A) 20 & 60 2 6
(B) 20 & 80 2 8
(C) 30 & 60 3 6
(D) 40 & 80 4 8
(E) 50 & 100 5 10
Only 8 is 2Â³ two more factos then 2

I didn't get your point here. What is your answer?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 am; Thanked: 47 times; Followed by:2 members

by kstv » Tue Mar 16, 2010 6:27 am

IMO B cos
A )6 = 2*3
B) 8 = 2 * 2 * 2 (two more factors)
C) 6 = again 3*2
D) 8 = 4* 2
E ) 10 = 5*2

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Tue Mar 16, 2010 6:30 am

kstv wrote:IMO B cos
A )6 = 2*3
B) 8 = 2 * 2 * 2 (two more factors)
C) 6 = again 3*2
D) 8 = 4* 2
E ) 10 = 5*2

I guess you misinterpreted something.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Tue Mar 16, 2010 6:30 am

sanju09 wrote:Two different numbers have the same prime factors, but one of the numbers has two more factors than the other. Which of the following would correctly represent the two numbers?
(A) 20 & 60
(B) 20 & 80
(C) 30 & 60
(D) 40 & 80
(E) 50 & 100

40 has 8 factors and 80 has 10 . No of prime factors for both of them are 2 ( 2 & 5).

IMO D .

Regards,
Harsha

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[email protected]: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Tue Jan 19, 2010 11:15 pm; Location: India; Thanked: 2 times

by [email protected] » Tue Mar 16, 2010 8:52 pm

sanju09 wrote:Two different numbers have the same prime factors, but one of the numbers has two more factors than the other. Which of the following would correctly represent the two numbers?
(A) 20 & 60
(B) 20 & 80
(C) 30 & 60
(D) 40 & 80
(E) 50 & 100

IMHO Answer is B

Because

20 = 5 X 2 X 2
80 = 5 X 2 X 2 X 2 X 2 (2 more factors)

All other choices have only one factor extra.

What is the OA ???

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Wed Mar 17, 2010 2:21 am

[email protected] wrote:
sanju09 wrote:Two different numbers have the same prime factors, but one of the numbers has two more factors than the other. Which of the following would correctly represent the two numbers?
(A) 20 & 60
(B) 20 & 80
(C) 30 & 60
(D) 40 & 80
(E) 50 & 100
IMHO Answer is B

Because

20 = 5 X 2 X 2
80 = 5 X 2 X 2 X 2 X 2 (2 more factors)

All other choices have only one factor extra.

What is the OA ???

Please revise this concept with an example as under:

How to find total number of factors of a number, say 56

Step 1: Break 56 into its primes, like 56 = 2 Ã— 2 Ã— 2 Ã— 7 = 2^3 Ã— 7^1

Step 2: Add 1 to each exponent of the primes, 3 + 1 = 4 and 1 + 1 = 2

Step 3: Multiply the results of Step 2 together, 4 Ã— 2 = 8

Hence, the total number of factors of 56 is 8.

We can count those for 56

1, 2, 4, 7, 8, 14, 28. and 56; out of which exactly two (2 & 7) are prime factors of 56; exactly 6 (2, 4, 7, 8, 14, & 28) are proper factors of 56.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Fiver: Master | Next Rank: 500 Posts; Posts: 114; Joined: Mon Sep 22, 2008 3:51 am; Thanked: 8 times; GMAT Score:680

by Fiver » Wed Mar 17, 2010 2:45 am

harshavardhanc wrote:
sanju09 wrote:Two different numbers have the same prime factors, but one of the numbers has two more factors than the other. Which of the following would correctly represent the two numbers?
(A) 20 & 60
(B) 20 & 80
(C) 30 & 60
(D) 40 & 80
(E) 50 & 100
40 has 8 factors and 80 has 10 . No of prime factors for both of them are 2 ( 2 & 5).

IMO D .

Same soln.
Agree with D.

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GMATSUCKER: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sat Feb 27, 2010 2:58 am; Location: GMAT

by GMATSUCKER » Wed Mar 17, 2010 2:57 am

Is this a real GMAT Question ?

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