GMAT Data Sufficiency Discussions

23. At a certain bookstore, each notepad costs x dollars and each markers costs y dollars.
If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4
markers instead?
1). each notepad cost less than $1
2). $10 is enough to buy 11 notepads

I'm getting a D...

1) Let's take the exytreme cases...if N = 1$

then from stem M = 5/3$

to test it further the condition..

4N + 4M = 4*1+5/3*4 > 10..

lest take next case N = 0

M = 10/3$

4N + 4M = 10*4/3$ > 10...

A is sufficient...

OA is E)...could you please explain?
1) x^2 is +ve #==> x is +ve or -ve

2)x.y is not +ve # ==> x is zero or -ve

1 & 2 ==> x is -ve , Hence option C

^ +1 agreed !!!!

If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x, y and y - 2 is x.
(2) The average (arithmetic mean) of x and y is not an integer.
Puys..help me out 2 sort out d ans...

OA-> A
My ans -> E

If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x, y and y - 2 is x.
(2) The average (arithmetic mean) of x and y is not an integer.
Puys..help me out 2 sort out d ans...

OA-> A
My ans -> E


statement 1: (x+y+y-2)/3 = x

x+2y-2=3x

2y-2 = 2x

y-1 = x

Since x is an integer Y is also an integer. Sufficient

Statement 2 is insufficient

Ans: A

A)
(X+Y+Y-2)/3 = X
---> 2X=2Y-2, ---> X = Y-1

as X is integer, Y is also an integer

Sufficient

B) we cannot say X is an integer. It can be real number also.

Insufficient

In a certain bookstore, each notepad costs x dollars and each markers costs y dollars.
If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4
markers instead?
1). each notepad cost less than $1
2). $10 is enough to buy 11 notepads



1). each notepad cost less than $1
2). $10 is enough to buy 11 notepads

1) Use two ends of extremes.

If Notepad cost = 0.99, then Marker cost is around 1.66, making it impossible to buy 4 Note pads and 4 Markers

If Notepad cost = $0.5, and the marker cost is $1 (the question stem says $10 is 'enough'). In this case with $10 we can buy 4 notepads and 4 markers

---> INSUFFICIENT

2) By the same logic as mentioned in case 1, it is not clear whether we can buy 4 notepads and 4 markers

---> INSUFFICIENT

Ans is: E
In a certain bookstore, each notepad costs x dollars and each markers costs y dollars.
If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4
markers instead?
1). each notepad cost less than $1
2). $10 is enough to buy 11 notepads


1). each notepad cost less than $1
2). $10 is enough to buy 11 notepads

1) Use two ends of extremes.

If Notepad cost = 0.99, then Marker cost is around 1.66, making it impossible to buy 4 Note pads and 4 Markers




---> INSUFFICIENT

2) By the same logic as mentioned in case 1, it is not clear whether we can buy 4 notepads and 4 markers

---> INSUFFICIENT

Ans is: E

If Notepad cost = $0.5, and the marker cost is $1 (the question stem says $10 is 'enough'). In this case with $10 we can buy 4 notepads and 4 markers
I guess this isn't true....
if Notepad = 0.5 => Marker = 2.5

For the Notepad prblm, my take is option E

There can be 2 possibilities with both the statments combined

y = 2 ; x = .8 (8 + 1.6 )
y = 3 ; x = .2 ( 12 + .

So my take is option E

23. At a certain bookstore, each notepad costs x dollars and each markers costs y dollars.
If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4
markers instead?
1). each notepad cost less than $1
2). $10 is enough to buy 11 notepads

I'm getting a D...

1) Let's take the exytreme cases...if N = 1$

then from stem M = 5/3$

to test it further the condition..

4N + 4M = 4*1+5/3*4 > 10..

lest take next case N = 0

M = 10/3$

4N + 4M = 10*4/3$ > 10...

A is sufficient...

OA is E)...could you please explain?


My take : option-> E

Heres another one..

If x and y are positive. is y
(1) x > 2y
(2) x + 2


Bit confused wid d OA.. plz sort it out.. OA later..

Taking only (1)x = 4 y = 1
x = 9 y = 3 .Nt suff

Taking only (2) x = 2 y = 3
x = 1 y = 1 Nt suff

Combining both statements,we get x= 1 and y=0.But q states y as positive. 0 is neither + nor - confused.

Anyways I will go with option C

Heres another one..

If x and y are positive. is y
(1) x > 2y
(2) x + 2


Bit confused wid d OA.. plz sort it out.. OA later..



IMO C

From 1) we have the condition where y> 2 and y
Fro m2) we have a condition where y>2 and y
Combining both we have y
In a certain bookstore, each notepad costs x dollars and each markers costs y dollars.
If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4
markers instead?
1). each notepad cost less than $1
2). $10 is enough to buy 11 notepads



1). each notepad cost less than $1
2). $10 is enough to buy 11 notepads

1) Use two ends of extremes.

If Notepad cost = 0.99, then Marker cost is around 1.66, making it impossible to buy 4 Note pads and 4 Markers

If Notepad cost = $0.5, and the marker cost is $1 (the question stem says $10 is 'enough'). In this case with $10 we can buy 4 notepads and 4 markers

---> INSUFFICIENT

2) By the same logic as mentioned in case 1, it is not clear whether we can buy 4 notepads and 4 markers

---> INSUFFICIENT

Ans is: E


The question says " is $10 enough to buy 4 notepads and 4
markers instead" .

So it is enough to find out whether 4x+4y=10.

Now from 1) we have x
so from the info abv we can see that we can 4 note pads and 4 markers as it costs less than 10 dollars. So suff


Take 2) we have x = 10/11. so from this we have y = 20/11 so subs these values in 4x+4y=10 we have 120/11 so we cannot buy 4 markers and 4 notes pads. So suff

Hence D.
IMO C

From 1) we have the condition where y> 2 and y
Fro m2) we have a condition where y>2 and y
Combining both we have y

Hey siddharth..
plz clarify ..

y>2 and YIs Y ?

Im confused.. OA is C but wid d same conclusion i marked E.
Hey siddharth..
plz clarify ..

y>2 and YIs Y ?

Im confused.. OA is C but wid d same conclusion i marked E.

If x and y are positive. is y
(1) x > 2y
(2) x + 2

from 1 we can write the ineq as x-2y>0. but we have multiple scenarios here
such as x= 51 and y = 25; x = .9 and y = 0.4

so insuff

from 2) we can write the eq as x-y-20

here also we get multiple scenarios like 1) so insuff.

combining both and solving for y

we get y
I hope you understood.
The question says " is $10 enough to buy 4 notepads and 4
markers instead" .

So it is enough to find out whether 4x+4y=10.

Now from 1) we have x
so from the info abv we can see that we can 4 note pads and 4 markers as it costs less than 10 dollars. So suff


Take 2) we have x = 10/11. so from this we have y = 20/11 so subs these values in 4x+4y=10 we have 120/11 so we cannot buy 4 markers and 4 notes pads. So suff

Hence D.


Hi Siddarth,
combining both the statements we can have 2 possibilities

1. y = 2 ; x = .8 (8 + 1.6 ) $10 is suff
2. y = 3 ; x = .2 ( 12 + . 0.4) $10 is insuff.

So even combining both the statements we cannot ans the q.
Hi Siddarth,
combining both the statements we can have 2 possibilities

1. y = 2 ; x = .8 (8 + 1.6 ) $10 is suff
2. y = 3 ; x = .2 ( 12 + . 0.4) $10 is insuff.

So even combining both the statements we cannot ans the q.



Can you plz elaborate?
siddharthaduggirala Says
Can you plz elaborate?


Hi Siddarth,
We have to match 3 conditions namely :

1.5x + 3y = 10
2. x 3. 11x
With the above conditions we need to check if 4x+4y

We have two sets of values matching all the above conditions

a) x = 0.8 & y = 2. With this combination we will have 4x+4y b) x = 0.2 & y = 3. With this combination we will have 4x+4y > 10 .So $10 is not suff to buy the items

So we can't conclude even after combining both the statements.
crushkiller Says
^ +1 agreed !!!!

amsey1382 Says
Answer is E)..


Earlier I missed a case (in red)

1) x^2 is +ve #==> x is +ve or -ve

2)x.y is not +ve # ==> x can be zero , -ve and +ve(if y=0)

1 & 2 ==> x can be zero , -ve and +ve , Hence option E
Hey siddharth..
plz clarify ..

y>2 and YIs Y ?

Im confused.. OA is C but wid d same conclusion i marked E.


Simple Explaination:

Combining 1 & 2 you have --> 2y
if y=3 --> 6 y=2 --> 4 y=1 ---> 2 y=1.9 -->3.8=> y