12 Days of Christmas GMAT Competition - Day 10: If x and y are : Data Sufficiency (DS)

**Bunuel** · Dec 23, 2022

12 Days of Christmas GMAT Competition with Lots of Fun

If x and y are non-zero integers, is

?

(1)

(2)

This question was provided by GMATWhiz
for the 12 Days of Christmas Competition.

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Spoiler: OA

**Bunuel** · Dec 24, 2022

Bunuel wrote:12 Days of Christmas GMAT Competition with Lots of Fun

If x and y are non-zero integers, is ?

(1)

(2)

This question was provided by GMATWhiz
for the 12 Days of Christmas Competition.

Win $30,000 in prizes: Courses, Tests & more

GMATWhiz Official Explanation:

Step 1: Analyse Question Stem

x and y are non-zero integers
We are given x/30+y/50=10
Since y is an integer, therefore 5x/3 has to be an integer for which we can assume x=3k where k is non-zero integer
Plugging x = 3k, we get y=500-(5×3k)/3 ⇒ y=500-5k
So, for x/30+y/50=10 to exist, the value of x and y has to be of the form 3k and 500 – 5k respectively

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: x + y = 500

If x=3k and y=500-5k is true:
So, x=3k and y=500-5k is not true
Thus statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2: y – x = 20

If x=3k and y=500-5k is true:
Thus statement 2 alone is not sufficient

Hence the right answer is Option A.

**Kinshook** · Dec 23, 2022

Asked: If x and y are non-zero integers, is

?

Is 5x + 3y = 1500 ?

(1)

3x + 3y = 1500
Since x is non-zero
5x + 3y = 2x + 3x + 3y = 2x +1500 > 1500
SUFFICIENT

(2)

Case 1: -
3y - 3x = 60
8x + (3y-3x) = 5x + 3y = 8x + 60 = 1500
8x = 1440
x = 180
y = 200

Case 2: -
x = 1
y = 21
5x + 3y = 5 + 63 = 68 < 1500
NOT SUFFICIENT

IMO A

**Surerere** · Dec 23, 2022

X and Y is non zero and asking about validation about
x/30 + y/50 = 10
So this clear it's not a equation, it's a question

Now com to 1st equation
x+y= 500

Can this validate above equation now simplify question equation
5x+3y=1500
So not possible by Alon

Now com to 2nd equation
y-x=20

So also Alon can not validate

Now take both together so we find 2 equation together so we can find value of x and y then can validate the equation.

So Ans- C

Posted from my mobile device

**thisisit25** · Dec 23, 2022

If x and y are non-zero integers, is

Reframing the equation: 5x + 3y = 1500
We need to check what are the combinations based on the statements that make this equation work.

(1) x+y=500
x = 500-y
Replace in main equation:
5(500-y) + 3y = 1500 ?
2500 - 5y + 3y = 1500 ?
2500 - 2y = 1500?
There are many values possible for 2500 - 2y for different integer values of y. Let's assume it is 1500. Solving for y = (2500-1500)/2 = 500 = integer
May or may not be 1500.

Not sufficient.

(2) y–x=20
y = 20+x
Replace in main equation:
5x + 3(20+x) = 1500 ?
8x + 60 = 1500 ?
There are many values possible for 8x + 60 for different integer values of x. Let's assume it is 1500. Solving for x = (1500-60)/8 = 180 = integer
May or may not be 1500.

Not sufficient.

(1) + (2)
x+y=500
–x + y=20
y = 520/2 = 260 = integer.
x = 500-260 = 240

Now 5x + 3y will give a unique value to answer the question!

Sufficient.

**Archit3110** · Dec 23, 2022

given that x & y are non zero integers
is

#1

given
5x+3y = 1500
from #1
we get
4x+2y = 1000
2x+y = 500
for +ve integers x is 0 and y is 500
not possible
insufficient
#2

y= x+20
5x+60+3x = 1500
x = 180 & y = 200
sufficient
OPTION B is correct

Bunuel wrote:12 Days of Christmas GMAT Competition with Lots of Fun

If x and y are non-zero integers, is ?

(1)

(2)

This question was provided by GMATWhiz
for the 12 Days of Christmas Competition.

Win $30,000 in prizes: Courses, Tests & more

**Nandini2242** · Dec 23, 2022

If x and y are non-zero integers, is x30+y50=10x30+y50=10?

(1) x+y=500

(2) y–x=20

If we manipulate the question stem, we get 5x + 3y = 1500. Clearly, this doesn't help us. (Remember this is still a question, i.e., is 5x + 3y = 1500?)

1. Looking at option one we can write x in terms of y or y in terms of x, but we can't find he value of 5x + 3y.
NOT SUFFICIENT

2. This is also Not Sufficient for the same reason as 1.

Statements together:-
Adding the 2 statements will give us value of y. From this we can find x and solve the question. (Keep in mind we don't need to actually solve as this a data sufficiency question)

C is our answer.

**UtkarshAnand** · Dec 23, 2022

Bunuel wrote:12 Days of Christmas GMAT Competition with Lots of Fun

If x and y are non-zero integers, is ?

(1)

(2)

This question was provided by GMATWhiz
for the 12 Days of Christmas Competition.

Win $30,000 in prizes: Courses, Tests & more

Solution:
Given, x and y are non-zero integers

?
or 5x + 3y = 1500?

Statement (1)

Multiplying the equation by 3 we have, 3x + 3y = 1500. This when compared to 5x + 3y = 1500 has a difference of 2x unaccounted for.
As x and y are non-zero integers, clearly 2x will have some value and hence, either 5x + 3y>1500 or 5x + 3y<1500. But 5x + 3y cannot equal 1500 (as x cannot be equal to 0).
Sufficient.

Statement (2)

As the difference is given, we cannot manipulate the statement to arrive at something similar to question statement, 5x + 3y = 1500. Clearly, insufficient.

ANSWER A.

**kavitaverma** · Dec 23, 2022

IMO A

1. (5x + 3y)/150 = (3(x+y) + 2x) / 150 = (1500 +2x)/150
so the value will be either less than 10 or more than 10 in case x is -ve or positive. But since we know that x is not zero, the term cannot be 10.
Sufficient.

2. Insufficient.

**singhaz** · Dec 23, 2022

x/30 + y/50 =10

it means we need to check whether 5x + 3y =1500

both statements tells us about this hence D

**akhtolkhyn** · Dec 23, 2022

(1) x+y=500
x/30+y/50= (50x+30y)/150=(5x+3y)/150=(5/3x+y)/50;
10=(x+y)/50; (5/3x+y)/50 = (x+y)/50 can not be equal so sufficient
(2) y–x=20
x/30+y/50=(y-x)/2 We can not find whether this equations are equal or no. So not sufficient

IMO A

**SauravSah** · Dec 23, 2022

Simplify the equation given in the stem:

x/30+y/50=10
(50x+30y)/1500=10
50x+30y=15000
10(5x+3y)=15000
5x+3y=1500

Statement 1:
x+y=500
x=500-y

5(500-y)+3y=1500
2500-5y+3y=1500
-2y=1000
y=500

Putting value of y in in above equation for x,
x=500-500=0

5*0+3*500=1500
1500=1500 (Sufficient)

Statement 2:
y-x=20
y=20+x

5x+3(20+x)=1500
5x+60+3x=1500
8x=1440
x=180

Putting the value of x in above equation for y,
y=20+180=200

5*180+3*200=1500
900+600=1500
1500=1500 (Sufficient)

Answer: D

**samagra21** · Dec 23, 2022

S1) x=100, y=400, x/30+y/50 is not 10.
For integers, Only (0, 500) makes the exp 10. But x cannot be 0.

Hence Suff

S2) Taking close numbers such that diff is 20,
x=30, y=50, x/30+y/50=1
x=180, y=200, x/30+y/50=6+4=10 , Not Suff

Hence Ans is A)

**Catman** · Updated on: Dec 24, 2022

If x and y are non-zero integers, is

+

=10?

On simplyfying the equation, we get

5x+3y=1500

Statement 1 : x+y=500

Using statement 1 we get 3x+3y=1500 Now for this and 5x+3y=1500 to be true x=0, but since x and y are non- zero integer.
So

+

is not equal to 10.

Statement 2: y–x=20

Using statement 2 and y-x=20, we get y=200 and x=900/5 Thus for these value

+

is equal to 10, but X and Y are integer.

Hence IMO Choice A

Last edited by Catman on 24 Dec 2022, 11:15, edited 1 time in total.

**Kushchokhani** · Dec 23, 2022

Given that x, y are integers other than 0
Q: is 5x+3y=1500?

Statement 1:
x+y=500
i.e. 3x+3y=1500
and since x is not 0, 5x+3y can never be 1500
Answer is always NO to the ques. Hence, this statement alone is sufficient.

Statement 2:
y=x+20
Substituting this in Q, we get 5x+3(x+20)
=> 5x+3x+60
=> 8x+60
So, after substituting, effectively, ques asks us whether x=1440/8=180?
We are not sure about that. Hence, this statement alone is not sufficient.

Answer is A.

**Elite097** · Dec 23, 2022

If x and y are non-zero integers, is x30+y50=10x30+y50=10?

(1) x+y=500---- The stem is only true if y=500 and x=0 (simulatenously) but we know x cannot be 0 hence no combo of x and y can give the desired result. Sufficient

(2) y–x=20-- NS
If y =40, x=20 then no
If y=200, x=120 yes (solve simultaneously to gt this)

Ans A

**LeopardLiu** · Dec 23, 2022

Answer is A
If x and y are non-zero integers, is x/30+y/50=10?
From the question, we can get 5x + 3 y = 1500

(1) x+y=500 we can get 3x+3y=1500. Sufficient

(2) y–x=20 insufficient.

**kratos0906** · Dec 23, 2022

Considering statement (1),
x+y=500
Dividing both sides by 50,
\frac{x}{50} + \frac{y}{50} = 10

So, we can conclude that \frac{x}{30} + \frac{y}{50} is not equal to 10.

So, (1) is enough.

Considering statement (2),
y-x=20
Since there is a negative sign involved, we can't conclude anything about \frac{x}{30} + \frac{y}{50}.

So, (2) is not enough.

Hence, IMO A.

**pintukr** · Dec 23, 2022

If x and y are non-zero integers, is x/30 + y/50 = 10?

YES/NO DS question

(1) x + y=500

There are multiple (x,y) pairs possible for x + y=500

However, true for only one pair ie, x=0; y = 500----> YES
NOT true for other pairs eg x=300; y = 200----> NO

Hence, INSUFFICIENT

(2) y – x=20

Similarly here, there are multiple (x,y) pairs possible for y – x=20

However, true for only one pair ie, x=180; y = 200----> YES
NOT true for other pairs eg x=130; y = 150----> NO

Hence, INSUFFICIENT

(1) & (2) together

ie, x + y=500
– x + y =20

This leads to x=240; y =260
For this specific pair of values; x/30 + y/50 'NOT equal to' 10

So, the answer is NO

Hence, SUFFICIENT

Hence, the correct answer will be (C)

**limuengaoey** · Dec 23, 2022

If x and y are non-zero integers, is x/30+y/50=10

(1) x+y=500
I is insufficient because x and y can be varied to make the equation become true
hence A and D are wrong
(2) y–x=20
II is wrong with the same reason hence B is also wrong.

From I and II we know the exact number for x and y.
Hence we can demonstrate whether the question is true or not.
Therefore,C is the answer

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