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Hi! In my son's maths exam paper there was this question: Pls tell me what will be the correct answer and why?

  • Hi! In my son's maths exam paper there was this question: Pls tell me what will be the correct answer and why. Any one option has to be selected. Q - A number is exactly divisible by 56 if it is divisible by both: (A) 7,8 (B) 2,28 (C) 4,14 (D) 3,15 This is a class VI maths final exam paper.

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    7 and 8 They are both factors of 56 that don't share a common factor themselves, if you want the reason Edit: Because 28 is divisible by 2 and 28 but not 56, 84 is divisible by 14 and 4 but not 56, and 3 and 15 is just dumb. 7 and 8 don't share a factor AND they're least common multiple is 56, so a number divisible by both of them MUST be divisible by 56 Edit 2: It's badly worded, and you thus misunderstood it, which is understandable. You see, 2, 28 and 4, 14 as common factors both contain possible numbers that AREN'T divisible by 56, so you can't just say a number is divisible by 56 if it's divisible by both, say, 4 and 14, because you could think of examples that disprove that. If you want it in pure logic terms, as in p -> q, then observe this: "If a number is divisible by both 4 and 14, then it's divisible by 56." This is false due to the aforementioned example of 84, and other numbers as well, so "q" is false in this case. the same is true of 2 and 28; it's not always true that a number divisible by 2 and 28 is also divisible by 56. However, it IS true with 7 and 8

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7,8 l.c.m of 7,8 is 56

SK

This question is wrongly worded. When you say that there is a number 'exactly divisible by 56', it means that the divisor is 56; then it has to be a number necessarily larger than 56, e.g. 112 or 168. No such option is given of a larger number. On the other hand, if you want to say 'divisors of the number 56', then the answers could be either A or B or C. Thirdly, if the question were worded 'NOT exactly divisible OF the number 56', then the option would be 'D' !

TimeLess1

1) Without any second consideration the choice only A (7, 8). Reason: i) LCM of the pair (7, 8) only is 56; where in LCM of the pair (2, 28) and (4, 14) is only 28 and not 56. As such all those divisible by 56 are definitely divisible by 28 but vice verse is not true. ii) Similarly all those numbers which are divisible by 56 will definitely be divisible by all its factors. However vice verse is not true. iii) Further, 56 is an even multiple of 28; as such only those numbers which are even multiple of 28 would be divisible by 56 and not all multiples of 28.

Learner

The answer is (A) 7, 8 It can neither be (B) 2, 28 nor (C) 4, 14 because they have a common factor 2. Consider the number 84. It is divisible by both 2 and 28, and, 4 and 14. Yet not divisible by 56. To check for exact divisibility, one has to take all the factors of the divisor that do not have common factors among them!

Panpa

OK. Usually you try to find prime multiples that will end up being the GCM..greatest common multiple. In this case the answer is A even though it could have been (7,2)..since both are prime. The others are reducible to lower multiples.

Adrian S

Option (A) - 7, 8 . A number is exactly divisible by 56 if it is divisible by both 7 and 8 because 56 = 7*8 and they are mutually prime i.e. they have no common factor.

Dambarudhar

The factors of 56 as listed are 28,14,8,7,4,2 so answers A,B,C all apply. There's apparently no single answer so this may be some kind of "trick"

Domenic

D

mofizul

Wow typical indian worried mother....great...its 7 and 8 mam.....:)

Ashu, sensibly insane

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