Is x less than y? (1) x - y + 1

Question

Is x less than y?

(1) x - y + 1 < 0
(2) x - y - 1 < 0

DS26402.01

Bunuel · Accepted Answer

Is x less than y? Is x is x-y<0 ? (1) x-y+1<0 --> x-y<-1 . Sufficient. (2) x-y-1<0 --> x-y<1 . Not sufficient. Answer: A.

BrentGMATPrepNow · Answer

Target question: Is x < y?

Statement 1 : x-y+1<0 
Add y to both sides to get  x+1  < y
Since x <  x + 1 , we can write: x <  x+1  < y
From this, we can definitely see that   x < y 
So, statement 1 is SUFFICIENT

Statement 2 : x - y - 1 < 0 
Add y to both sides to get  x - 1  < y
Since  x - 1  < x, 
We can see that y and x are both greater than  x - 1 , but we can't tell whether   x < y 
So, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

amma4u · Answer

yes A it is

1.) x-y<-1 This is satisfied when x<y

2.) x-y<+1 Not sufficient

example x=1.5 and y=1; 1.5-1 < 1
 x = - 2 and y= -1; -2 - (-1) < 1

A it is.

mandyrhtdm · Answer

That's a very easy trap to fall for, I to fell for it.
Added the two inequalities and got x-y <0 and condluded both are necessary
But if you look at x-y +1 < 0 this means that x+y < -1 
which means that X-Y < 0 as -1 < 0 , so we can get the answer from one only.

Now looking at 2) X-Y -1< 0 this means that x-y < 1 which doesn,t clearly mean that x<y as something less than 1 can be positive and negative both.

So A is the answer.
Damn i need more practice !

EvaJager · Answer

(1)  x-y+1<0  implies  x-y<-1<0 , which means  x-y<0  or  x<y .
Hence sufficient.

(2) Take  x = y = 0  for which obviously x is not less than y, but (2) holds. For x = 0 and y = 1, (2) still holds, but now x < y.
Not sufficient.

Answer A.

msk0657 · Answer

Given x>y

Then we need to find x-y > 0 ?

Stat 1: x-y-1>0 
 => x-y > 1...Sufficient.

Stat 2: x-y + 1 > 0.
 => x-y > -1... Insufficient ( Since we need to seek x-y > 0 )

Thus A is correct answer.

Silviax · Answer

The way you explained makes a lot more sense than the official explanation of Magoosh.

I can now see that statement 1 is sufficient by itself. 
Thanks!

MathRevolution · Answer

Now we will solve this DS question using the Variable Approach

You can visit https://www.mathrevolution.com to learn and master this Approach along with other tips to quickly solve DS questions.

The first step of the Variable Approach: Modify the original condition and the question to suit the type of information given in the conditions. This is a priority and the most important step. The first step alone gives us a 30% chance of answering the question correctly.

=> We have to find whether x is less than y?

We have to apply CMT 1 as we are looking for a yes or no answer.

=> Is x < y => Is x - y < 0

Lets look at Condition (1) : It tells us that x - y + 1 < 0

=> Rearranging gives: x - y < - 1 that tells us x - y is less than '0'

Since the answer is yes, the condition is sufficient by CMT 1 which means that the answer must be in terms of a unique yes or no.

Lets look at Condition (2) : It tells us that x - y - 1 < 0

=> Rearranging gives: x - y < 1

=> If x = 2 and y = 1.5 then x - y = 2 - 1.5 = 0.5 < 1 but 0.5 is not less than 0 [NO]

=> But if x = - 2 and y = 1.5 then x - y = -2.5 - 1.5 = -4 < 1 and it is less than 0 [YES]

So we will not get a unique value. So, the condition is not sufficient by CMT 1 which means that the answer must be in terms of a unique yes or no.

Condition (1) ALONE is sufficient.

So, A is the correct answer.

Answer: A

In about 30% of cases, just knowing the first step of the Variable Approach will get you to the correct answer.

dave13 · Answer

Bunuel what if for ST 1 i have 4-6 < 1 then y could be -6 and x could be 4

then x is more than y

Bunuel · Answer

In your example, y is 6 not -6.

Basshead · Answer

Is x less than y?

x < y?

(1) x - y + 1 < 0
x + 1 < y

SUFFICIENT.

(2) x - y - 1 < 0

x - 1 < y

We can't conclude if x < y. INSUFFICIENT.

Answer is A.

RICKY2020 · Answer

x = - 2 and y= -1; -2 - (-1) < 1 but will not this results to (-2+1<-1 ?)

bumpbot · Answer

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Is x less than y? (1) x - y + 1 < 0 (2) x - y - 1 < 0

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