If y is greater than 110 percent of x, is y greater than 75 ? : Data Sufficiency (DS)

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17 Jan 2014, 11:53

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Bunuel

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If y is greater than 110 percent of x, is y greater than 75 ?

(1 ) x > 75
(2) y -x = 10

y > 1.1 * x

Statement 1) x > 75 as y > 1.1 * 75, definitely we can say y > 75. Sufficient

Statement 2) y - x = 10 => y = 10 + x . As we don't know the value of x, we cannot determine if y > 75. Not Sufficient.

Hence Option A)

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23 May 2014, 10:55

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If y is greater than 110 percent of x, is y greater than 75 ?

1. x > 75
2. y -x = 10

Ans:

1: Clearly sufficient

2: y= 10+x => x=y-10 and also y>1.1x so y>1.1(y-10) -----> 110>y. Thus not sufficient.

A it is!

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23 May 2014, 11:03

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If y is greater than 110 percent of x, is y greater than 75 ?

1. x > 75
2. y -x = 10

1. Is sufficient enough to declare that y>75

2. In-sufficient

Hence, I go with option A.

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23 May 2014, 11:47

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If y is greater than 110 percent of x, is y greater than 75 ?

Looking at options
(1). x> 75
As y >1.1 x --> y >75. Sufficient

(2). y -x =10
As y >1.1 x --> x = y/1.1 - d where d >0
So, (2) --> y - y/1.1 + d = y/11 + d = 10 --> y = 110 - 11d
So, y > 75 will depend on the value of d; Not sufficient
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07 Dec 2014, 11:20

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[youtube][/youtube]This question always leave me wondering.
What we know from the test of the problem: y > 1.1x

1) x > 75 and y > 75*1.1
So y > 82.5 and the statement is sufficient.

2) y - x = 10 and, since we are interested in the limiting case, y = 1.1*x
So 1.1x - x = 10, x = 100 and y = 110, leading to y > 110.

Why the reasoning behind the second point is wrong according to the GMAT Quant Review?

Only now I saw why.

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07 Jun 2015, 04:30

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Y>1.1X,
Is Y > 75?

1. X>75
Put x=75, Y>82.5, definitely y is greater than 75

Sufficient

2. Y-X= 10
X=Y-10
Y>1.1(Y-10)
Y>1.1Y - 11
0.1Y<11
Y<110
Not Sufficient

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30 Aug 2017, 20:34

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Bunuel

SOLUTION

If y is greater than 110 percent of x, is y greater than 75 ?

Given: $y>1.1x$.
Question: is $y>75$? Or is $x\geq{\frac{75}{1.1}}$

(1) x > 75. Sufficient.

(2) y - x = 10. Not sufficient as shown above.

Answer: A.

Hi Bunuel,

Can you pls point out the flaw in my reasoning.
Given that y>1.1x
As a limiting case, suppose y=1.1x
So, if y-x=10
0.1x=10
x=100
y>1.1x -> y>110
Isn't it suff??

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20 Jul 2018, 13:30

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srikanth9502

Bunuel

SOLUTION

If y is greater than 110 percent of x, is y greater than 75 ?

Given: $y>1.1x$.
Question: is $y>75$? Or is $x\geq{\frac{75}{1.1}}$

(1) x > 75. Sufficient.

(2) y - x = 10. Not sufficient as shown above.

Answer: A.

Hi Bunuel,

Can you pls point out the flaw in my reasoning.
Given that y>1.1x
As a limiting case, suppose y=1.1x
So, if y-x=10
0.1x=10
x=100
y>1.1x -> y>110
Isn't it suff??

Can someone please explain? Why is y>110 incorrect?

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15 Feb 2019, 18:23

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Bunuel

SOLUTION

If y is greater than 110 percent of x, is y greater than 75 ?

Given: $y>1.1x$.
Question: is $y>75$? Or is $x\geq{\frac{75}{1.1}}$

(1) x > 75. Sufficient.

(2) y - x = 10. Not sufficient as shown above.

Answer: A.

Hi Bunuel! Is it ok to say that 110>y and because of that, B is no sufficient?

Thank you in advance!

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18 Aug 2019, 07:13

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srikanth9502

Bunuel

SOLUTION

If y is greater than 110 percent of x, is y greater than 75 ?

Given: $y>1.1x$.
Question: is $y>75$? Or is $x\geq{\frac{75}{1.1}}$

(1) x > 75. Sufficient.

(2) y - x = 10. Not sufficient as shown above.

Answer: A.

Hi Bunuel,

Can you pls point out the flaw in my reasoning.
Given that y>1.1x
As a limiting case, suppose y=1.1x
So, if y-x=10
0.1x=10
x=100
y>1.1x -> y>110
Isn't it suff??

Hi srikanth9502 , Xin Cho

We have given y>1.1x
It means y can be 1.2x, 1.3x and so on...

Now as a limiting case i.e. y=1.1x
you already got y>110 .
But what about other cases i.e. when y=1.2x, 1.3x, 1.4x

Now if you will check for all values you will see the value of x keep on decreasing and so on for y.
Hence it(y>75) is not true in every case. That's why B is insufficient.

Hope it helps

Let me know for anything else.

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18 Aug 2019, 08:12

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Aha, I missed this. Thank you for the explanation a12bansal.

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09 Mar 2021, 00:41

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Bunuel EducationAisle where am I going wrong?

Given: Y > 1.1x
To find: Is y > 75?

(1) x > 75

Clealry if x > 75 and since y > 1.1x then y > 75

(2) y - x = 10

Let's say y = 1.1x, in that case 1.1x - x = 10 OR x = 100. i.e x > 75. With the same logic in (1) we can say that (2) is suff.

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10 Mar 2021, 04:14

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Hoozan

(2) y - x = 10

Let's say y = 1.1x, in that case 1.1x - x = 10 OR x = 100. i.e x > 75. With the same logic in (1) we can say that (2) is suff.

Yes, in this case, y > 75.

However, please also note that the question just says that y > 1.1 x.

So, y can also be 2x. So, if we assume y = 2x,

2x - x = 10
x = 10

Substituting x = 10, we get in y > 1.1 x, we get y > 11. This could mean y > 75 or it could mean y < 75.

So, (2) is not sufficient.

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16 Jun 2021, 04:07

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Bunuel

If y is greater than 110 percent of x, is y greater than 75 ?

(1) x > 75
(2) y -x = 10

Solution:

Question Stem Analysis:

We need to determine whether y is greater than 75, given that it’s greater than 110% of x.

Statement One Alone:

Since x > 75 and y > 1.1x, then y > 1.1(75) = 82.5. Since y > 82.5, then y > 75. Statement one alone is sufficient.

Statement Two Alone:

Since y = x + 10 and y > 1.1x, we have:

x + 10 > 1.1x

10 > 0.1x

100 > x

We see that x < 100. However, we can’t determine whether y > 75. For example, if x = 70, then y = 1.1x = 77. However, if x = 60, then y = 1.1x = 66. In the former case, y > 75; in the latter case, y < 75. Statement two alone is not sufficient.

Answer: A

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24 Jun 2022, 10:28

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avigutman

Hi Avi,

Is there any logical way to solve statement 2?
Can we use number line to say that when ratios (y:x) and difference btw 2 no. (y-x) are given, it is difficult to say how far y is from zero.

Thanks in advance.

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Sneha2021

Is there any logical way to solve statement 2?
Can we use number line to say that when ratios (y:x) and difference btw 2 no. (y-x) are given, it is difficult to say how far y is from zero.

The problem is we're actually not given a ratio - we're given an inequality of a ratio. And, the question itself is also an inequality. So, we have to do a bit of math, unfortunately.
By the way, Sneha2021, if we did know the values of y:x and (y-x), we would be able to find the values of x and y.

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Hi avigutman - qq on the yellow highlight

The yellow has a % change (Specifically the underlined phrase - Greater than 110 percent )

Thus thought it would better to change to Change factor. instead of % change(greater than 110 percent )

Change factor for "greater than 110 percent" is (x 2.1) per my understanding

Quote:

If y is greater than 110 percent of x, is y greater than 75 ?

Thus I thought the yellow statement could be re-phrased as

if, y > (change factor) of x
or
if, y > (2.1) of x

I noticed though from other experts, the re-phrase should be instead : y > (1.1) of x

If y is greater than 110 percent of x, is y greater than 75 ?

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If y is greater than 110 percent of x, is y greater than 75 ?

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