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This is a little bit of a puzzle and a little bit of quiz. [#permalink]
03 Feb 2005, 13:21

This is a little bit of a puzzle and a little bit of quiz. You may solve it if you take plenty of time but the point here is to solve it within 2 mins. So plz do time yourself.
Here it goes:

Someone asked me, "what are the ages of your 3 daughters?".
I replied, well I won't tell you directly but 'd give you clues. Everytime I give you a clue you'd have to tell me if it is sufficient or not. So here goes our conversation.

I: The product of the ages of my daughters is 36
S: Well not sufficient. Give me the 2nd clue.

I: The sum of their ages is same as the numerical address of my next door neighbour.
S goes out checks the address but still could not tell. He asks for the 3rd and final clue

I: My eldest daughter is sleeping in the next room.
S in no time tells me the ages of my daughters.

Question: What are the ages of my daughters.

P.S If someone already knows the answer, plz keep it to himself and skip this quiz. Once again it is doable (if such a word exists) in 2 mins. Just think logically.

answer is 1 4 and 9. Explaination later. I took around 5 mins to do it.

I am sorry to write 1 4 9 in hurry the ans should be 2 3 6

The explaination comes here.....

when he says the product is 36.. then the combinations are as follows:

AGES THEIR SUM

1 6 6 sum = 13
1 4 9 sum = 14
1 3 12 sum = 16
1 2 18 sum = 21
2 3 6 sum = 11
3 3 4 sum = 10
1 1 36 sum = 38

Now in the second clause he says see the address of next door. This means the sum of the ages was one less than the address of the left next door and one more than right next door.
So we need to choose the combinations from the above sum

There are two such combinations
I 11 and 13 where his house no must be 12
II 14 and 16 where his house no must be 15

thus after knowing the next door nos he still cannot choose the combination of their age

Now the third clause said that the eldest daughter is sleeping inside which conveys that the age of the eldest and second eldest daughter is not the same which is a clue for the I combination 11 and 13
where 2 3 6 sums to be 11
and 1 6 6 sums to be 13

the II combination gets no clue from III clause so it is not to be considered....

Vijo, I thought about that too. The problem is he says he went out and checked the address, but he didn't say which address he checked. By using single "my next door neighbor" it looks like he only have one neighbor. But if he only checked the address of the owner's house instead of the neighbors then you could be right. Still there's the issue that lots of street you got even numbers on one side and odd numbers on the other side.

in my opinion he checked the left neighbour which has the number 34 on the even side of the road, so we can assume that the man has the number 36 and that his right neighbour has the number 38 and 38 is also the sum of the ages of 3 girls 1+1+36

the big problem is that this system works for many other cases but i don't see why this answer should not be accepted

2 things also :

1. I am also wondering if there is any connection between "next neighbour" and :"next room" so that the man is in fact checking the number of his elder daughter...

2. In the question : Everytime I give you a clue you'd have to tell me if it is sufficient or not so I imagine we can find it from the second clue maybe...

The key is that he can see the number. So say if the number is 38, he'd immediately which set of numbers is the one that he wants. The only case that he wouldn't know for sure, is when the sum number is the same for two sets. That's why he needed a third clue.

Ages of my daughters are :--- [#permalink]
04 Feb 2005, 06:49

Well I liked the reasoning of all you guys. Pretty analytical. Infact that's the way to approach the problem.The key here is to realize that the 2nd clue is most vital. So the way to do is :
Clue 1. product 36 of 3 nos. ==> find the set of 3 factors (25- 30 secs).
Clue 2. A bit tricky but most important ==> Knowing the sum is not sufficient to tell the factors ==> there must be two combinations of factors which have identical sum or else he'd have told the answer (30-40 secs) only when the sum is 13 so either 1,6,6 or 2,2,9
clue 3. Nail on the coffin ==> Bingo, eldest (forget about twins and other considerations since the answer is unique don't complicate it further) ==> 2,2,9 (10 secs)

One thing I have observed and also learnt from a close friend of mine is that it is always critical to take time and answer the toughest of questions since that'd put you in a higher bracket. Also there is no such thing as 37 questions in 75 mins in Quant.
Reason being it is a CAT exam. My friend who scored 760 finished his CAT GMAT in 1 hour 40 mins (the entire test). He got only 18 or so questions in quant. He said since he kept on answering it correctly the computer gave him tougher and tougher questions and the computer knows by as many tough questions correctly answered where the candidate stands. In fact his 18th question was on Quantum Mechanics, he solved that too and the section got over at that point. Well that doesn't mean you have to learn quantum mechanics it just means that if you end up answering 37 questions in your GMAT your score will be less than 700 for sure since you 'd have made a few wrong answers.

Other important thing which I learnt is that a tough question is at times 3 or 4 times the weightage of a easy or medium level one.

The computer treats SC as easy question and there is more penalty for making a mistake on easy question ==> If you think of scoring 710 + there is no way you can make a mistake on SC. Period.

I have never heard of this -- that you can get less than 37 q's in quant...
I think there have been several members of the GMAT club who scored 760+, but none recounted that the quant section could be less than 37 q's.
Is this true?

Well then I think it beats the very purpose of CAT. Then it means there is no limit to difficult questions in the CAT bank. Because all the computer does is to test how good you know. If you can do a really tough question then obviously you'd be able to do an easy one. In other words one who gets 760 should be good enough for getting 650 also. what does the computer learn from the candidate if he keeps on answering all the questions beyond a reasonable doubt that he is doing each correctly. And the GMAT CAT questions are typically in 4 or 5 rungs say x-2,x-1,x,x+1,x+2 is the guy has answered 10 questions in x+2 correctly what'd the point then if there is no x+3 level??????????

Let me know. I might have been wrongly told by the guy then.

Re: Ages of my daughters are :--- [#permalink]
04 Feb 2005, 09:07

anirban16 wrote:

In fact his 18th question was on Quantum Mechanics, he solved that too and the section got over at that point.

Incorrect. There is no Quantum Mechanics questions in GMAT. You need to reread your OG.

Quote:

if you end up answering 37 questions in your GMAT your score will be less than 700 for sure since you 'd have made a few wrong answers.

Incorrect. There WILL be 37 questions no matter how well you answered them. And you CAN get a score above 700 even if you made a few mistakes.

Quote:

The computer treats SC as easy question and there is more penalty for making a mistake on easy question ==> If you think of scoring 710 + there is no way you can make a mistake on SC. Period.

Most likely incorrect. It's true that if you make many mistakes on easy questions, the chances are that you are not going to get many higher level questions that has a greater weight, thus it is likely that you won't get a very high score. However a couple mistakes on simple SCs may not be deadly. In addition, I'm highly suspicious about the claim that all SCs are treated as easy questions.

Thanks for clearing my doubts.
Well regarding the problem about Quantum Mechanics well I framed it wrongly. What he meant was that it needed to be solved using quantum mechanics, the conventionals way 'd take way too long.

I need to check back with this guy. But he did tell me that he was surprised when his math section answered after he solved this difficult one and he did finish the test in 1 hour 45 mins (Verbal + quant).

gmac.com explicitly states that there will be 37 ques in math, no matter how good u r. My suggestion is to value every ques type and give ur best in each and every type of ques in both section and forget abt the rest. Let ETS ppl do their job. No need to analyze which ques is considered easy, difficult etc, there is no way for anyone to know, not even Kaplan, PR et al.

I agree. Well so that's that. 37 questions in 75 mins difficult or easy depending on how you perform. But definitely the questions can't go beyond a certain level of difficulty if you question each of the previous questions correctly and hence timing is very important. I was thinking take your time to solve the tricky ones just make no mistake but now it appears that you better do it in 2 mins.

I agree. Well so that's that. 37 questions in 75 mins difficult or easy depending on how you perform. But definitely the questions can't go beyond a certain level of difficulty if you question each of the previous questions correctly and hence timing is very important. I was thinking take your time to solve the tricky ones just make no mistake but now it appears that you better do it in 2 mins.

What do ya say?

Anirban

Yep, 2 - 3 min max....remember, there can also be some 6-7 weird experimental ques mixed in the section. These ques do not count towards ur result, so if u happen to spend 5 mins to these kinda ques, thinking they will improve ur score, then it might backfire. My theory is to give ur best shot to every ques for 3 min max, if u can't figure out an approach to crack it then probably u will not be able to even in 5 mins.

so that means of 37 questions in any section not all is going to count. So even if you made 5 mistakes in each you might end up getting 800 since you made a mistake only in the experimental questions.

But now suppose you make a mistake in a difficult (but experimental) question u answered wrongly the next question is easier you answer it correctly the next difficult question is again experimental and again you made a mistake. So it may be possible that I mean to make things simpler for the PC only easy or medium questions are experimental since it is no point in giving a difficult experimental question if the computer doesn't learn anything about the candidate from it.