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# If k is a common multiple of 75, 98, and 140, which of the

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Intern
Joined: 01 Jul 2013
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Schools: LBS MIF '15
If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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15 Oct 2013, 05:14
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66% (02:02) correct 34% (01:59) wrong based on 837 sessions

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If k is a common multiple of 75, 98, and 140, which of the following statements are true?

I. k is divisible by 9
II. k is divisible by 49
III. k is greater than 14,000

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III
Manager
Joined: 13 Aug 2012
Posts: 86
Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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15 Oct 2013, 06:19
14
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Prime factors:-
$$75= 3*5*5$$
$$98= 2*7*7$$
$$140= 2*2*5*7$$
$$LCM= K= 2*2*3*5*5*7*7= 14700$$
I) K cannot be divisible by 9 since only a 3 is the factor of 14700
II) K is divisible by 49 as is evident by the two 7s
III) K>14000

So only (II) and (III) are always true hence the answer D
##### General Discussion
Intern
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Posts: 27
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
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Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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15 Oct 2013, 05:55
4
1
bulletpoint wrote:
If k is a common multiple of 75, 98, and 140, which of the following statements are true?

I. k is divisible by 9
II. k is divisible by 49
III. k is greater than 14,000

a) II only
b) III only
c) I and II only
d) II and III only
e) I, II, and III

Given K is a common multiple of 75,98,140, Least Common Multiple of these numbers will be 14700
K will be of the form 14700*n...where n=1,2,3,.....

I)14700*n is not divisible by 9 for all values of 'n' (eg: at n=1,k=14700 not divisible by 9). Hence I cant be always true
II) 14700*n is divisible by 49 for all values of 'n'. Hence II is true
III)14,700*n is greater than 14,000.Hence III is true

Ans d) II and III only
Hope its clear
Director
Joined: 23 Jan 2013
Posts: 507
Schools: Cambridge'16
If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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08 Nov 2014, 07:39
3
2
Prime factorization:

75=5*5*3
98=2*7*7
140=5*2*2*7

1) k is divisible by 9: NO, there is no prime factors of 9, i.e 3*3
2) k is divisible by 49: YES, there is 7*7=49
3) k>14,000: LCM=49*25*4*3=49*300=50*300>14,000, so YES

D
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Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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27 Jul 2015, 04:01
Math Expert
Joined: 02 Sep 2009
Posts: 64244
Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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27 Jul 2015, 04:11
4
honchos wrote:
If k is a common multiple of 75, 98, and 140, which of the following statements are true?

I. k is divisible by 9
II. k is divisible by 49
III. k is greater than 14,000

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III

III to be true it should be mentioned that k is a positive integer. For example, 0 is a common multiple of 75, 98, and 140 and is NOT greater than 14,000.

Rare example of flawed question from GMAT.
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Status: Verbal Forum Moderator
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Posts: 448
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GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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27 Jul 2015, 04:20
Bunuel wrote:
honchos wrote:
If k is a common multiple of 75, 98, and 140, which of the following statements are true?

I. k is divisible by 9
II. k is divisible by 49
III. k is greater than 14,000

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III

III to be true it should be mentioned that k is a positive integer. For example, 0 is a common multiple of 75, 98, and 140 and is NOT greater than 14,000.

Rare example of flawed question from GMAT.

I was also astonished it was an exam pack questions.
Intern
Joined: 01 Apr 2015
Posts: 45
If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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Updated on: 29 Jul 2015, 06:11
Bunuel, since its asking which of the following are true and NOT 'must be true'. This question seems legit, don't you think ?

Because i have seen official questions always mention 'must be true' if they are asking for only must be true answers, for example: Refer OG 13- PS- 221, but you are the Gmat Guru so please correct me if I'm wrong.

Thanks.

Originally posted by Swaroopdev on 29 Jul 2015, 06:06.
Last edited by Swaroopdev on 29 Jul 2015, 06:11, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 64244
Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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29 Jul 2015, 06:08
Swaroopdev wrote:
Bunuel, since its asking which of the following are true and NOT 'must be true'. This question seems legit, don't you think ?

Because i have seen official questions always mention 'must be true' if they are asking for only must be true answers, but you are the Gmat Guru so please correct me if I'm wrong.

The question asks "which of the following statements are true?", which is equivalent to "which of the following statements must be true?". If it were otherwise it would be "which of the following statements could be true?"
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Intern
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Posts: 45
Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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29 Jul 2015, 06:20
Bunuel, so it is either 'could be true' or 'must be true' and not as this question states. Got it.

Thanks.
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Posts: 301
Location: United States
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Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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29 Jul 2015, 16:55
Swaroopdev wrote:
Bunuel, so it is either 'could be true' or 'must be true' and not as this question states. Got it.

Thanks.

Swaroopdev I'm sorry, but I don't understand what the difference of meaning is when "must" is left out. I suppose without "must" there is less emphasis, but other than that, the meaning is the same.
Intern
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Posts: 2
Schools: HEC Jan'16
Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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30 Jul 2015, 04:24
honchos wrote:
Bunuel wrote:
honchos wrote:
If k is a common multiple of 75, 98, and 140, which of the following statements are true?

I. k is divisible by 9
II. k is divisible by 49
III. k is greater than 14,000

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III

III to be true it should be mentioned that k is a positive integer. For example, 0 is a common multiple of 75, 98, and 140 and is NOT greater than 14,000.

Rare example of flawed question from GMAT.

I was also astonished it was an exam pack questions.

Bunuel, Calculating LCM of 75,98 and 140 is 14700 which is least,so how can you say zero is a common multiple? Please correct me if I am wrong.
Math Expert
Joined: 02 Sep 2009
Posts: 64244
Re: If k is a common multiple of 75, 98, and 140, which of the  [#permalink]

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30 Jul 2015, 04:37
1
1
onlynk1 wrote:
honchos wrote:
Bunuel wrote:
If k is a common multiple of 75, 98, and 140, which of the following statements are true?

I. k is divisible by 9
II. k is divisible by 49
III. k is greater than 14,000

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III

III to be true it should be mentioned that k is a positive integer. For example, 0 is a common multiple of 75, 98, and 140 and is NOT greater than 14,000.

Rare example of flawed question from GMAT.

I was also astonished it was an exam pack questions.

Bunuel, Calculating LCM of 75,98 and 140 is 14700 which is least,so how can you say zero is a common multiple? Please correct me if I am wrong.

Notice that we are told that k is a common multiple of 75, 98, and 140 NOT the least common multiple of 75, 98, and 140. By default, the least common multiple is considered to be the least common positive multiple, because otherwise it does not make any sense.

For example, the LCM of 2 and 3 is 6, which means that 6 is the least common positive multiple of 2 and 3. If we were allowed to consider negative multiples too, then there won't be an answer.

Back to the question:
1. 0 is a multiple of every integer, so 0 is a common multiple of every non-zero sets of integers.
2. 0 is not the only common multiple of 75, 98, and 140, less than 14,000, so is -14,700, -2*14,700, -3*14,700, -4*14,700, ...

Hope it's clear.
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Re: If k is a common multiple of 75, 98, and 140, which of the   [#permalink] 30 Jul 2015, 04:37