manpreetsingh86 wrote:
hi mike, thanks for responding and clearing the air regarding the question. i got this question, from one of my friend, who is also preparing for gmat at the well known institute over here in india.
well, regarding the solution. this is how, i responded to this question.
Rule : All numbers whose digits are same and are in a multiple of six will always be divisible by 7,11 and 13. thus 111111,111111111111 will always be divisible by 7,11 and 13.
so, we can quickly zero down to number 111111. we can see this number is not divisible by 49. thus 777777 is our lucky number. next, by using the rule mentioned above, without doing any calculation we can see that it will be divisible by 11 and 13. also since, sum of its digits is a multiple of 3. therefore, it will be divisible by 3. thus, without touching any calculator we can zero down to 4 distinct prime factors. now as far as the fifth prime factor is concerned, we can focus on the unit digit( which is 7) of original number.
now, unit of 7^2=9, 13=3,3=3 and 11=1
thus unit digit of product of 3,7^2,11 and 13 is 1, thus our next prime must have a unit digit of 7. thus our first two possible choices are 17 and 37. we will first divide the number by 17. we will see, its not divisible by 17. next we will divide the number by 37 and bingo.
As can be see, until the last step,we are not required to do any calculation.
P.S. : this is an unsolved question. i've pinged the link of the same question to the mike for his consideration.
If this is the kind of questions the institute is passing off as GMAT questions, you really need to worry whether you (or your friend) are in the right hands. As a test maker, I can tell you that it is very easy to make hard questions. The problem lies in making simple questions which seem hard - the requirement of GMAT. The problem lies in making them GMAT relevant!
There is no logical way forward in this question. N is a multiple of 49 with all its digits same. There are innumerable numbers with all digits same - 22, 222, 2222, 3, 33, 333, 3333, 33333, 33333333 etc.
One cannot pick up a random rule and take that as starting point. We encourage people to understand logic, not learn up rules. Here, the question requires one to learn up obscure rules. Even if one does know that 6 digit numbers with all same digits will be divisible by 7, how do you know that a number such as 9999 is not divisible by 49 without calculating?
Mind you, rules can come in handy. In fact, I will give you a question I made for which this rule is relevant. But knowing the rule only hastens your solving, not knowing is not an impediment. Try this:
Question: On multiplying a positive integer N having n digits by (n + 2), we get a number with (n + 1) digits, all of whose digits are (n + 1). How many such N exist?
(A) None
(B) 1
(C) 2
(D) 8
(E) 9
There is a logical starting point here which gives you a range of only a few numbers. You ignore some of them using logic. You work on only a few and find your answer.
hi karishma, thank you very much for responding. well i'm not taking any coaching from any institute and i'm not associated with any coaching institute. usually, when we prepare for something, we tend to share our knowledge about the subject with other people. my friend has got this question, from his faculty. he put the same question to me. so, i thought of discussing the same here in this forum. i don't see any harm in doing such thing. Also, because i'm not an expert, so therefore don't know which question qualifies as gmat type and which doesn't.
well, this is definitely not some random rule. i know about these stuff and other rules, back from my olympiad days. i thought others might be aware of it, if not, then they might learn something new today.