GMATPrepNow wrote:
skywalker18 wrote:
I think the keyword here is that the number is divided successively .
Let x be the number which when successively divided by 4 and 5 gives 1 and 4 as remainder.
1. When we first divide the number by 4 .
x = 4y +1
where y is quotient from the first division
2. Now as the division is done successively , we divide the quotient from the first step by 5
y= 5z +4
where z is quotient from the second division
If Z=1 ,
y = 9
x= 9*4 + 1
= 37
Now , on dividing the by 20 , we get 17
Answer E
Alternatively , we can also proceed from the final quotient .
Let x be the quotient after dividing the original number by 5.
So , the number which we divided by 5 to yield a remainder of 4 = 5x+ 4
This number 5x+4 is the quotient from the first division of the original number by 4
Therefore , the number should be = 4(5x+4) + 1
= 20x +17
We can clearly see that when divided by 20 , we should get a remainder of 17
Answer E
I have to admit that, when I saw the word "successively," I thought that this might be what it means. However, I soon discounted that possibility and assumed the intent of the question was to tell us that, "
When a certain number is divided by 4 and 5, the remainders are 1 and 4 respectively"
Here's why I discounted the other possibility:
In order for us to proceed as you have suggested above, we must ignore some important information. For example, let's divide 49 "successively" by 5 and 3. First, 49 divided by 5 equals 9 with remainder 4. This means that 49 divided by 5 equals 9 4/5. Now, we must take the result and divide by 3. You are suggesting that we take 9 and divide by 3. What about the the remainder of 4? What do we do with that? Alternatively, what do we do with the 4/5? We ignore it? What is there in the question that tells us to ignore the remainder from the first division?
We could also note that dividing a number successively by 5 and 3, is the same as dividing a number by 15. If we divide 49 by 15, we get a remainder of 4. If we apply the operations as you suggestabove, we get a remainder of 0.
The concept of successively dividing only seems to make sense (in my opinion) if the original number is divisible by BOTH divisors. For example, it makes sense to say that dividing 48 successively by 3 and 2 yields a result of 8. That is, 48/3 = 16 and 16/2 = 8.
Ignoring a certain component (i.e., the remainder) of the first division when performing the second division is not stated anywhere in the question. Given this, I don't think this could ever be an official GMAT question. I have certainly never seen a similar question. Have any other experts seen an official question of this nature?
Cheers,
Brent
Hi Brent,
If we take 37 as the original dividend and proceed with this question-
1. Dividing by 4
---------Q------------R
37/4 --- 9 --------- 1 -- 9*4 + 1 = 37
or ----- 9.25 ------ 0 -- 9.25*4 = 37
2. Dividing by 5
---------Q----------R
9/5 --- 1 --------- 4
or 9.25/5------ 1.85------ 0
3.On Dividing 37 by 20
---------Q----------R
37/20 --- 1----- 17
or ------1.85 ----- 0
In my opinion we can either express division -
1.As an integer quotient Q and a remainder R( which might be equal to 0)
2.Or as a decimal / fraction quotient Q, but in this case the remainder R will be always 0 .
But , we can't do both - have a decimal / fraction quotient and a remainder .
In general , we use method 1 and even here we are given a remainder .
If we use method 2 , we will get the same quotient after steps 1-2 and in step 3 , but the remainder will always be 0 .
The numbers used are similar to the one's suggested by you - dividing 49 successively by 5 and 3 or dividing by 15 ,
as 20 can be expressed as 5*4 .
Just my 2 cents .
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