If 0

Question

If 0 < x < y, is y - x < 0.00005?

(1) x > 1/60,000

(2) y < 1/15,000

bicu17 · Accepted Answer

1) NS - nothing about y
2) NS - nothing about x

So it's between E and C

Is y-x < 1/20,000? 
LT = less than
GT = Great than
LT 1/15,000 - GT 1/60,000 < 1/20,000. Multiply by 60,000 to simplify results in LT 4 - GT 1 < 3? Test extremes - 3.9 - 1.1 = 2.8 . YES ...sufficient. C

Bunuel · Answer

If 0 1 --> if x=2 and y=3 then the answer is YES but if x=2 and y=5 the answer is NO. Not sufficient. (2) y < 4 --> if x=2 and y=3 then the answer is YES but if x=0.5 and y=3.5 the answer is NO. Not sufficient. (1)+(2) Remember we can subtract inequalities if their signs are in opposite directions --> subtract (1) from (2): y-x<4-1 --> y-x<3 . Sufficient. Answer: C.

KarishmaB · Answer

There are two ways to deal with it. Method 1: Is y-x < 0.00005? We can see that both statements alone are not sufficient. (1) x>1/60,000 (2) y<1/15,000 We know that we can add inequalities when they have the same sign ie. a < b c < d then, a+c < b+d Also, when we multiply an inequality by -1, the inequality sign flips. x>1/60,000 implies -x < -1/60,000 You can add these two inequalities: -x < -1/60,000 and y<1/15,000 to get y-x < 1/15000 - 1/60,000 which is y-x < 1/20,000 i.e. y-x < 0.00005 Another method is to see this on the number line. Draw a number line to understand this. 01/60,000 means x lies to the right of 1/60,000 (2) y<1/15,000 means y lies to the left of 4/60,000 So the distance between them must be less than 4/60,000 - 1/60,000 = 3/60,000 = .00005

smyarga · Answer

(1) Insufficient. We know nothing about  y .
(2) Insufficient. We know nothing about  x .

(1)+(2) Sufficient. 
We know that  y<\frac{1}{15,000}  and  -x<-\frac{1}{60,000} . If we add this two inequalities we will get:
 y-x<\frac{1}{15,000}-\frac{1}{60,000}=\frac{1}{20,000}=0.00005

The correct answer is C.

Edofarmer · Answer

How do you know what sign the combined inequality takes when combining two inequalities with different signs?

Bunuel · Answer

ADDING/SUBTRACTING INEQUALITIES 1. You can only add inequalities when their signs are in the same direction: If a>b and c>d (signs in same direction: > and > ) --> a+c>b+d . Example: 3<4 and 2<5 --> 3+2<4+5 . 2. You can only apply subtraction when their signs are in the opposite directions: If a>b and c and < ) --> a-c>b-d ( take the sign of the inequality you subtract from ). Example: 3<4 and 5>1 --> 3-5<4-1 . Check for more the links below: Inequalities Made Easy!

dave13 · Answer

VeritasKarishma  (see highlighted) can you explain highlighted / i mean why you write "y lies to the left of  4/60,000 " and not "y lies to the left of 1/15,000"

x is greater than 1/60,000 so x can have many options same logic applies to Y if y<1/15,000 then can take numerous values

my question is why did you take these values to determine answer ---> 4/60,000 - 1/60,000 = 3/60,000

KarishmaB · Answer

dave13 :
I want to make the fractions comparable and want to be able to perform operations on them. When are two fractions comparable? They are intuitive to compare and we can perform operations on them when they have the same denominator.

One fraction given is 1/60,000.

Another fraction given is 1/15,000. So I multiply and divide it by 4 to get 4/60,000. Since I multiply and divide by the same number, the fraction does not change. 
1/15,000 = 4/60,000

Now I can easily perform operations on 1/60,000 and 4/60,000.

ag153 · Answer

1. What is the number line logic?

2. Also how are we subtracting the 2 statements and using the sign of the inequality it is subtracted from? What is the logic

avigutman · Answer

Elite097  Draw 0, x, and y from left to right as described in the free info.
The question is about the distance between x and y. We know that y sits to the right of x, and the question is whether the distance between them is "microscopic." 0.00005 = 5/100,000 = 1/20,000. Neither statement can possibly be sufficient on its own, because we're interested in the distance between x and y. Combining the statements may be useful, as we're given a bottom limit for x and an upper limit for y, forcing the distance between them to be  less than  some quantity. What quantity, exactly? Well, (1/15,000 - 1/60,000). Let's expand by a factor of 60,000 and infer that y-x < 3.
Rephrase the question, expanding by the same factor of 60,000 and get: Is y-x < 3? 
So the statements, combined, give us a definitive YES.
To your second question: Given two inequalities, we can reason that the sum of the bigger sides of the two inequalities must be greater than the sum of the two smaller sides of the two inequalities. If you want to subtract one inequality from the other, you can expand/reduce by a factor of (-1) the inequality that you wish to subtract (remembering to flip the sign, since the action you took flipped everything to the other side of zero, the mirror image), and then "add" the inequalities.

adgarg · Answer

After subtracting we only got that x-y<3 but how do we know that x-y is also less than 3/60000 ?

Bunuel · Answer

After rewrring the question we get:
 
 If 0 < x < y, is y - x < 3?

(1) x > 1 
(2) y < 4 
 
So, getting y - x < 3 gives a YES anwswer to that rephrased question.

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If 0 < x < y, is y - x < 0.00005? (1) x > 1/60,000 (2) y < 1/15,000

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