Is x – y ≥ 5 ? (1) x ≥ 9 (2) y ≤ 4

Question

Is x – y ≥ 5 ?

(1) x ≥ 9
(2) y ≤ 4

DS21189

Bunuel · Answer

Similar question: https://gmatclub.com/forum/is-x-y-5-1-x ... 24915.html

lacktutor · Answer

Is x – y ≥ 5 ?

(Statement1): x ≥ 9
No info about what y is. 
Insuffcient

(Statement2): y ≤ 4
No info about what x is. 
Insufficient

Taken together 1&2, 
x ≥ 9 
—y ≥ —4

Adding: 
x —y ≥ 5 (Always true) 
Sufficient

Answer (C)

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bM22 · Answer

Statement 1: x ≥ 9, Clearly Insufficient.
Statement 2: y ≤ 4, Clearly Insufficient.

Both Statements combined:
 x ≥ 9 & y ≤ 4.

Now 
x = 9, y = 4.
x – y ≥ 5. Condition is satisfied. 
But if, x= 9, y = -10. Again satisfied.

Answer C.

supriyap31 · Answer

Q : Is x – y ≥ 5 ?

St 1 : x ≥ 9
when y ≤ 4 condition satisfies , else condition does not satisfy.
Insufficient .

St 2 : y ≤ 4
for X ≥ 9 the value is satisfied, else the value is lesser than 5.
Insufficient .

Statement 1 and 2 taken together
x ≥ 9 and y ≤ 4
satisfies the above equation also derives :
x>=9 and y>= -4
Adding i and ii we get,
x —y ≥ 5 
Sufficient

Answer (C) both statements are sufficient together, but neither alone is sufficient.

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • We need to find out if  x – y ≥ 5

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  x ≥ 9
 • We know x ≥ 9, but we don’t know anything about y.
• Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  y ≤ 4
 • We know y ≤ 4, but we don’t know anything about x.
• Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining. 
 • From statement 1: x ≥ 9
• From statement 2: y ≤ 4
• On combining both statements, we get,
 o   x ≥ 9  
o  y ≤ 4  
o Now, the minimum value of x – y = the minimum value of x – the maximum value of y = 9 – 4 = 5
  Therefore,  x – y ≥ 5    
Thus, the correct answer is  Option C.

GMATinsight · Answer

Question: Is x - y ≥ 5?

Statement 1 : x ≥ 9

No information about value of y hence

NOT SUFFICIENT

STatement 2 : y ≤ 4

No information about value of x hence

NOT SUFFICIENT

COmbining the statements  
x ≥ 9 and y ≤ 4

For  (x-y)_{min}  we need to take Minimum value of x and Maximum Value of y

(x-y)_{min} = 9-4=5

i.e. x – y ≥ 5

SUFFICIENT

Answer: Option C

chetan2u · Answer

What does  x – y ≥ 5  mean?
It means 'is the difference between x and y ≥ 5, where x>y'.

Of course, we require to know the values of both x and y.

Do not waste time in the individual statements, as each gives you an inequality in just one variable.

Combined..
 x ≥ 9 and y ≤ 4.
Min value of x=9, and max value of y=4, so Minimum value of x-y=5, and x – y ≥ 5 will hold for all values of x and y.

Is x – y ≥ 5 ? (1) x ≥ 9 (2) y ≤ 4

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