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If a and b are both factors of 50, which of the following must be true
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09 Sep 2019, 21:07
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49% (01:41) correct 51% (01:34) wrong based on 106 sessions
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Competition Mode Question If a and b are both factors of 50, which of the following must be true? (A) ab≥ 2 (B) a + b≤ 50 (C) ab is a factor of 100. (D) ab is a factor of 2500. (E) ab is even.
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Re: If a and b are both factors of 50, which of the following must be true
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09 Sep 2019, 21:53
We are informed that a and b are factors of 50. We are to determine which of the answer choices must be true. factors of 50 are {1,2,5,10,25,50}. In A, we are given that ab≥2. This is not always true for the situation a=b=1, where ab=1. In B, a+b≤50. This also not always true for the situation a=25, and b=50, whereby a+b=75. In C, ab is factor of 100. This not always true for a=10 and b=25, where ab=250. In E, ab is even. This is not necessary true for a=1, and b=5, where ab=5, which is not even. In D, ab is a factor of 2500. This always true since taking the highest possible values that a and be can take, a=b=50, and computing ab=2500. In this case 2500 is a factor of 2500. Hence D must be true.
Answer is therefore D.



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Re: If a and b are both factors of 50, which of the following must be true
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09 Sep 2019, 22:18
50 has total 6 factors – 1, 2, 5, 10, 25 and 50. Since nothing is mentioned about relationship between ‘a’ and ‘b’ following conditions are possible: a. a > b b. a = b c. a < b where 1 ≤ a ≤ 50 and 1 ≤ b ≤ 50. Let’s test by invalidating ‘must be true’ for all possible conditions – Attachment: File comment: 50 has total 6 factors –
50 has total 6 factors.JPG [ 75.65 KiB  Viewed 1042 times ]
*  Since 2500 has total 15 factors which include all the 6 factors of 50, taking possible extreme values of ‘a’ and ‘b’ is sufficient.Answer (D).
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If a and b are both factors of 50, which of the following must be true
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Updated on: 10 Sep 2019, 23:13
If a and b are both factors of 50, which of the following must be true? Factors of 50: 1, 2, 5, 10, 25 and 50 (A) ab≥ 2  If a=1 and b=2, ab≥ 2 but if a=1 and b=1, then a<2.....no (B) a + b≤ 50  if a=50 and b=25, then no (C) ab is a factor of 100.  if a=25 and b=10, then no (D) ab is a factor of 2500.  if a=50 and b=25...yes ALWAYS (E) ab is even.  if a=1 and b=5, then no IMO answer is option D
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Originally posted by EncounterGMAT on 09 Sep 2019, 22:28.
Last edited by EncounterGMAT on 10 Sep 2019, 23:13, edited 2 times in total.



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Re: If a and b are both factors of 50, which of the following must be true
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10 Sep 2019, 04:09
Quote: If a and b are both factors of 50, which of the following must be true?
(A) ab≥ 2 (B) a + b≤ 50 (C) ab is a factor of 100. (D) ab is a factor of 2500. (E) ab is even. \(number.f(50)=(5^2,2)=(3)(2)=6\); and \(factors(50)=(1,50,2,25,5,10)\); \(a,b=any=(1,50,2,25,5,10)\) (A) ab≥ 2: \(a,b=(1,1):ab=1\) false (B) a + b≤ 50: \(a,b=(50,50):ab=2500\) false (C) ab is a factor of 100: \(a,b=(50,25):ab=1250\) false (E) ab is even: \(a,b=(1,1):ab=1\) false Answer (D)



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Re: If a and b are both factors of 50, which of the following must be true
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10 Sep 2019, 06:16
Factors of 50:2*5² Factors of 2500:2²*5⁴ So, all factors of 50 are factors of 2500 too. Option D Posted from my mobile device
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Re: If a and b are both factors of 50, which of the following must be true
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10 Sep 2019, 06:25
Prime factorization results to: 50 = 10*5 = 5*2*5 Thus, factors are: 1, 2, 5, 10, 25, 50 What must be true is that ab >= 2 since smallest factors are 1 and 2. So the correct answer should be A.



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Re: If a and b are both factors of 50, which of the following must be true
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10 Sep 2019, 10:19
If a and b are both factors of 50, which of the following must be true?
factors of 50 = 1, 2, 5, 10, 25, 50 some options were very easy to eliminate, the one that took time was A and D ...however, at the end , figured out
(A) ab≥ 2 a = 1, b = 1 1>=2 Not True
(B) a + b≤ 50 50+50 <= 50 > Not true
(C) ab is a factor of 100 50*50 is not a factor of 100 > Not true
(D) ab is a factor of 2500 50*50 is a factor of 2500 > True 1*1 is a factor of 2500 > True 2 * 25 is a factor of 2500 > True
(E) ab is even 25 * 5 is not even > Not true 1*5 is not even > Not true
D is the answer!



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Re: If a and b are both factors of 50, which of the following must be true
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10 Sep 2019, 11:37
Factors of 50 are {1, 2, 5, 10, 25, 50} Note: a & b can take same values!
(A) ab≥ 2 —> NO [(a, b) = (1, 1)] (B) a + b≤ 50 —> NO [(a,b) = (25, 50), (50, 50) etc.,] (C) ab is a factor of 100. —> NO [(a, b) = (50, 50) etc.] (D) ab is a factor of 2500. —> YES [Maximum value of ab = 50*50 = 2500, which is still a factor of 2500] (E) ab is even. —> NO [(a, b) = (1, 1), (5, 25) etc.]
IMO Option D
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Re: If a and b are both factors of 50, which of the following must be true
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10 Sep 2019, 23:32
Bunuel wrote: Competition Mode Question If a and b are both factors of 50, which of the following must be true? (A) ab≥ 2 (B) a + b≤ 50 (C) ab is a factor of 100. (D) ab is a factor of 2500. (E) ab is even. a is a factor of 50 b is a factor of 50 ab is a factor of 50*50 = 2500 IMO D
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Re: If a and b are both factors of 50, which of the following must be true
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17 Sep 2019, 09:49
Bunuel wrote: Competition Mode Question If a and b are both factors of 50, which of the following must be true? (A) ab≥ 2 (B) a + b≤ 50 (C) ab is a factor of 100. (D) ab is a factor of 2500. (E) ab is even. Since a is a factor of 50 and b is also a factor of 50, then ab is a factor of 50 x 50 = 2500. To eliminate the other choices,consider the factors of 50: 1, 2, 5, 10, 25, and 50. Choice A is incorrect because if a = 1 and b = 1, then ab = 1, and A is not true. Choice B is incorrect because if a = 50 and b = 10, then a + b = 60 and B is not true. Choice C is incorrect because if a = 25 and b = 10, then ab = 250, which is not a factor of 100. Choice D is true because every product of two factors of 50 is also a factor of 50 x 50 = 2500. Choice E is incorrect because if a = 1 and b = 5, then ab = 5, which is odd, so E is not true. Answer: D
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Re: If a and b are both factors of 50, which of the following must be true
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