x = 2y + z, where z

Question

x = 2y + z, where z < y. Find x.

1. When x is divided by y, it leaves 2 as the remainder.
2. When x is divided by y, it leaves a remainder which divides y without leaving any remainder and the quotient is 2.

LaxAvenger · Answer

Can someone post an explanation please?
I am having difficulties understanding the answer given that we do not know the value of z.

Bowtye · Answer

This question tests ones knowledge of the formula dividend = divisor * quotient + remainder

our formula in the question stem is x = 2*y + z . Does this look familiar?

So x is our dividend, y is our divisor, 2 is our quotient and z is our remainder.

Now lets look at our options

i) When x is divide by, it leaves 2 as the remainder.
 
 so what does this mean? it means that x= y*k + 2. Where k is some quotient. So we know that z = 2 but don't know anything about the quotient or y. insuff

ii) When x is divided by y, it leaves a remainder which divides y without leaving any remainder and the quotient is 2

what does this mean? lets take it one step at a time

1) x = yt+m (using t as the quotient so it does not get confused with k in the first statement) this just restates our formula dividend formula

2) Next we have that the remainder divides y without leaving a remainder and the quotient is 2. what does this look like?

y= 2m +0

3) Plug part 2 back into part 1 to get

x= 2m*t + m

Looking at the question stem, set t = 2 and we get x = 2m*2+m. This is insufficient because we don't know anything about the remainder.

Combining both i and ii

from part i we know the remainder is 2 and using our knowledge from part ii we get the formula x = 2*2*2+2 or x = 10

Sorry if this is complicated and not well written, I typed it on my phone and will clarify if yo have any further questions.

Thanks

varun2209 · Answer

NOTE: dividend=divisor*quotient + remainder
1) x=2y+z
 as per the statement 1 (dividing the expression by y)
 x/y= 2+z/y , leaves remainder 2, i.e z/y=2 (*NOTE)
 hence, x=2y+2 (insufficient since we dont know the value of y)
2) x=2y+z
 as per statement 2 (again dividing the expression by y)
 x/y= 2+z/y , 
 STATEMENT 2 IS A LITTLE TRICKY TO UNDERSTAND, 
 its says when x/y, it leaves a remainder which....divides y to leave no remainder and the quotient is 2
 so the remainder of x/y is z/y (as per *NOTE)
 i.e y/(z/y)=2 (insufficient)
 
 now combining 1) and 2) 
 from 1) we have z/y=2
 from 2) we have y/(z/y)=2 
 hence y=4
 so as per 1) we had x=2y+2 , hence x= 2*4+2 =10
 
 ans is C

PrepTap · Answer

Hi LaxAvenger

If x = 2y + z, and z < y, then z is the remainder when x is divided by y.

Statement 1: When x is divided by y, it leaves 2 as the remainder.
-> z = 2
x = 2y + 2 
Since we don't know y, we can't know x and therefore (1) is INSUFFICIENT.

Statement 2: When x is divided by y, it leaves a remainder which divides y without leaving any remainder and the quotient is 2.
-> (When x is divided by y, it leaves a remainder) which divides y without leaving any remainder and the quotient is 2
-> z (as we know that the remainder is z) divides y without leaving any remainder and the quotient is 2
-> y = 2z
x = 2y + z
x = 4z + z = 5z
Since we don't know z, this statement is also INSUFFICIENT.

When we combine (1) and (2), we can use z = 2 in the equation x = 5z 
-> x =10
SUFFICIENT
Therefore, C is the right choice here.

Hope that clears your doubt.

GMATinsight · Answer

Given: x = 2y + z, where z < y

Question: x=?

Statement 1: When x is divided by y, it leaves 2 as the remainder.

i.e. 2y + z when divided by x leaves remainder 2 but since 2y is divisible by y therefore we can conclude that
z when divided by y leaves remainder 2
but Since z<2 therefore z must be 2 itself as the quotient will be zero when z is divided by y

hence, we conclude that z = 2 but Since y is still unknown to calculate x therefore   NOT SUFFICIENT

Statement 2: When x is divided by y, it leaves a remainder which divides y without leaving any remainder and the quotient is 2

i.e. When 2y + z is divided by y, the remainder will be z only (because z<y and 2y is fully divisible by y)
and therefore, z divides y without leaving any remainder and the quotient 2 i.e.  y = 2z 
i.e. x = 2y + z = 2y + (y/2) = 5y/2
but Since y is still unknown to calculate x therefore    NOT SUFFICIENT

Combining both Statements: 
z = 2 and y = 2z and x = 5y/2

we get y = 4 and x = 10 i.e.   SUFFICIENT

Answer: Option  C

SOUMYAJIT_ · Answer

took me 3:42 to complete. Are these worth trying? Should I just make an educated guess in like 40 sec and move on?

hellosanthosh2k2 · Answer

x = 2y + z, z < y, x =?
z < y => when z is divided by y, remainder is z

Statement 1: When x is divided by y, it leaves 2 as the remainder.
=> x % z = 2
=> (2y + z) % y = 2
=> since 2y is multiple of y, remainder must be z (as z is less than y from question prompt)
=> so z must be 2 (from statement1)
=> x = 2y + 2 => still not suff, as we don't value of y

Statement 2: When x is divided by y, it leaves a remainder which divides y without leaving any remainder and the quotient is 2.
=> as we have seen from statement 1, when x is divided by y leaves remainder z
=> but it is mentioned, remainder z divides y evenly and leaves quotient 2
=> z is factor of y and y = 2z
=> x = 2y + z => x = 5z
=> still not sufficient, as we don't know value of z

Statement 1 + 2:
z = 2, x = 5z = 10
Sufficient => Answer (C)

Taikiqi · Answer

Good morning everyone,

I don’t quite understand the Statement 2, y=2z part. Can someone help?

Thanks.

Posted from my mobile device

bumpbot · Answer

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x = 2y + z, where z < y. Find x.

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