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Manager  Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India
The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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16 00:00

Difficulty:   65% (hard)

Question Stats: 65% (02:50) correct 35% (02:42) wrong based on 174 sessions

### HideShow timer Statistics The LCM and HCF of two numbers are 2376 and 22 respectively. Find the larger of the two numbers if their sum is 682.

A) 484
B) 562
C) 352
D) 576
E) 594

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Manager  Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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7
2
cleetus wrote:
The LCM and HCF o two numbers are 2376 and 22 respectively. Find the larger of the two numbers if their sum is 682.
A) 484 B) 562 C) 352 D) 576 E) 594

Methode 2
Now lets solve this using traditional way using variables Since the HCF is 22, Both the 2 numbers should be divisible by the HCF 22.
Let the two numbers by 22a and 22b where a and b do not have any common factor.
22ab = 2376
ab = 108

22(a+b) = 682
a+b = 31

Solving for ab=108 and a+b=31,
we get a=4 and b=27 or a=27 and b = 4
The larger among the two is 27*22=594
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##### General Discussion
Current Student Joined: 08 Jan 2009
Posts: 299
GMAT 1: 770 Q50 V46 Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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1
1
a x b = gcf(a,b) x lcm (a,b)
a x b = 2376 x 22 = 52,272 (last number ends in two)

Eliminate b,c,d as 1s digit won't work. Test a and e.

E works.

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Manager  Joined: 13 Jul 2011
Posts: 83
Concentration: Operations, Strategy
GMAT 1: 680 Q46 V37 WE: Engineering (Telecommunications)
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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1+ for E,
If A and B are two numbers whose LCM and GCF are 2376 and 22 respectively then AB = 2376*22 and A+B is 682 as given.
With this much info we can easily calculate A and B using brute force method and the answer is E.
Manager  Joined: 28 Sep 2011
Posts: 52
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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pike wrote:
a x b = 2376 x 22 = 52,272 (last number ends in two)

Eliminate b,c,d as 1s digit won't work.

Care to elaborate on this part?
Current Student Joined: 08 Jan 2009
Posts: 299
GMAT 1: 770 Q50 V46 Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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3
shanghaizzle wrote:
pike wrote:
a x b = 2376 x 22 = 52,272 (last number ends in two)

Eliminate b,c,d as 1s digit won't work.

Care to elaborate on this part?

When I saw this question, I wrote down the following:

a x b = 52272
a + b = 682

This is a clear constraint and its pretty simple to brute force the answer choices, but there is a further constraint, if we just focus on the ones digits.

If you think about multiplication we have: Or just focusing on the ones digits:
j x k = 2
j+k = 2

There is only one set of numbers, 8 and 4, which will fit that sub criteria. 8*4 = 2, 8+4 = 12.

We can see it like this: Hence we know that one of the numbers must end in either 8 or 4, and can eliminate b,c,d.

This just jumped into my mind straight away, I didn't spend too much time validating it as I knew brute force would work and I would know with certainty once I found an awer. So it was more a matter of giving me a head start in testing A and E. If it hadn't I would have just kept plugging.
Manager  Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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1
cleetus wrote:
The LCM and HCF o two numbers are 2376 and 22 respectively. Find the larger of the two numbers if their sum is 682.
A) 484 B) 562 C) 352 D) 576 E) 594

There are 2 approaches in solving this.
Methode 1.
HCF * LCM = The Actual Number.
2376 * 22 = 52272
So the answer which we are looking for has to be a factor of 52272.
So among the options shortlist the answers by eliminating those numbers which is not divisible by 52272. and then take the highest number as the answer as the question asks abt the highest number.
Here A and E are divisible by 52272 and since E is the highest, its the answer.
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Manager  Joined: 31 May 2011
Posts: 74
Location: India
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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2
4
cleetus wrote:
The LCM and HCF o two numbers are 2376 and 22 respectively. Find the larger of the two numbers if their sum is 682.
A) 484 B) 562 C) 352 D) 576 E) 594

This is how i solved it.

LCM: contains all factors excluding duplicates.
HCF: common factors

So factors of LCM (2376) are 2,2,2,3,3,3,11. These are the prime factors available in the two numbers.
But 22 is the HCF, so the remaining two numbers will have 2,2 and 3,3,3 as the remaining factors of the two numbers as the primes should be unique to each other. Else they would have been counted in the HCF.

So we have the two numbers as 22*2*2 = 88 and 22*3*3*3 = 594.
The process is pretty quick though Manager  Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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Thats pretty easy. Thanks for the explanation
+1 to u
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Intern  Joined: 25 Aug 2011
Posts: 19
Concentration: Entrepreneurship, General Management
GMAT Date: 01-31-2012
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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2
1
HI,

I did as follows:

a and bo both have to be multiples of 22, then:

682 - 22 = 660 --- not in answer choice
660 - 22 = 638 --- not in answer choice
638 - 22 = 616 --- not in answer choice
616 - 22 = 594 --- YES in answer choice

Manager  S
Joined: 23 Jan 2016
Posts: 180
Location: India
GPA: 3.2
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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Sudhanshuacharya wrote:
cleetus wrote:
The LCM and HCF o two numbers are 2376 and 22 respectively. Find the larger of the two numbers if their sum is 682.
A) 484 B) 562 C) 352 D) 576 E) 594

This is how i solved it.

LCM: contains all factors excluding duplicates.
HCF: common factors

So factors of LCM (2376) are 2,2,2,3,3,3,11. These are the prime factors available in the two numbers.
But 22 is the HCF, so the remaining two numbers will have 2,2 and 3,3,3 as the remaining factors of the two numbers as the primes should be unique to each other. Else they would have been counted in the HCF.

So we have the two numbers as 22*2*2 = 88 and 22*3*3*3 = 594.
The process is pretty quick though Hi,

How did you determine that the remaining numbers i.e 2^2 and 3^3 are unique to each number? Could it not be 22*2*3 and 22*2*3*3 or some other combination? Please help.
Intern  B
Joined: 25 Jan 2013
Posts: 29
Location: United States
Concentration: General Management, Entrepreneurship
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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OreoShake wrote:
Sudhanshuacharya wrote:
cleetus wrote:
The LCM and HCF o two numbers are 2376 and 22 respectively. Find the larger of the two numbers if their sum is 682.
A) 484 B) 562 C) 352 D) 576 E) 594

This is how i solved it.

LCM: contains all factors excluding duplicates.
HCF: common factors

So factors of LCM (2376) are 2,2,2,3,3,3,11. These are the prime factors available in the two numbers.
But 22 is the HCF, so the remaining two numbers will have 2,2 and 3,3,3 as the remaining factors of the two numbers as the primes should be unique to each other. Else they would have been counted in the HCF.

So we have the two numbers as 22*2*2 = 88 and 22*3*3*3 = 594.
The process is pretty quick though Hi,

How did you determine that the remaining numbers i.e 2^2 and 3^3 are unique to each number? Could it not be 22*2*3 and 22*2*3*3 or some other combination? Please help.

Because HCF is 22. Otherwise HCF would have been larger.
VP  P
Joined: 07 Dec 2014
Posts: 1212
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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cleetus wrote:
The LCM and HCF of two numbers are 2376 and 22 respectively. Find the larger of the two numbers if their sum is 682.

A) 484
B) 562
C) 352
D) 576
E) 594

if 682/22=31,
then larger number must be a multiple of 22≥16*22 that divides into 2376
only 594 fits
E
Non-Human User Joined: 09 Sep 2013
Posts: 11749
Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the  [#permalink]

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_________________ Re: The LCM and HCF of two numbers are 2376 and 22 respectively. Find the   [#permalink] 25 Aug 2018, 12:23
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