OG Quant supplement 2nd edition # 42

[GMATMadeEasy]

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

1. X > 75
2. Y - X = 10

Could someone explain the best way to deal with second statement ? I could solve the problem but looking from methodology perspective what strategy to employ such questions ?

Thanks.

[SoCan]

Since y>1.1x, the question is y>75 can be rephrased as is x>75/1.1 (not necessary to do the calculation)

To your question about the second statement - you have two expressions - y>1.1x and y=10+x. Plus in the value of y into the inequality:
10+x>1.1x
10>0.1x
100>x (which makes sense, because when x=100, y=1.1x, and for values of x greater than 100, y<1.1x.

Since x is less than 100, it could be greater or less than 75/1.1.

[cans]

y>1.1x. to find if y>75
a) x>75. as y>1.1x, thus y>75. sufficient
b) y-x=10
now x can take and value. suppose x=1,y=11 y<75
x=90,y=100 y>75. insufficient.
IMO A

[Anurag@Gurome]

Solution:
Consider first 1. Alone
X > 75. Or 1.1x > 1.1*75.
Now, y > 1.1*x.
Or y > 1.1*75.
Note that 1.1*75 > 75.
Or y > 75.
So, 1. alone is sufficient.
Next consider 2. alone.
This means that y = x + 10.
Or, 1.1*y = 1.1x + 11 < y + 11.
Or 1.1*y < y +11.
Or 0.1y < 11.
y < 110.
But we cannot say whether y > 75 or not.
So, (2) alone is not sufficient.

The correct answer is (A).

[Stuart@KaplanGMAT]

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

1. X > 75
2. Y - X = 10

Could someone explain the best way to deal with second statement ? I could solve the problem but looking from methodology perspective what strategy to employ such questions ?

Thanks.

Let's examine statement (2) conceptually rather than with equations.

(2) tells us that Y is 10 more than X. From the original, we know that Y is greater than 110% of X.

Since Y is greater than 110% of X, we know that Y is more than 10% more than X.

Putting that information together, we now know that 10 is more than 10% of X.

Well, if X=99, then 10 is more than 10% of x and Y>75.
However, if X=10, then 10 is more than 10% of X and Y<75.

So, (2) is insufficient to answer the question.

[pemdas]

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

1. X > 75
2. Y - X = 10

Could someone explain the best way to deal with second statement ? I could solve the problem but looking from methodology perspective what strategy to employ such questions ?

Thanks.

st(2) y=10+x and question says y>1.1x, So 10+x>1.1x translates into 0.1x<10 and x<100

To answer 'is Y greater than 75 ?' we have insufficient information as x can be 90 (x<100 and greater than 75), also x can be 10 (x<100 and less than 75)

[vikram4689]

Nice ques.... initially missed it by assuming y=1.1x only and thought that B is also suff. but y can be 110 x and then y<75.... Ans is A