Is the range of the integers 6, 3, y, 4, 5, and x greater

Question

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

(1) y > 3x
(2) y > x > 3

Bunuel · Accepted Answer

SOLUTION

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

Given integers are: {3, 4, 5, 6, x, y}

(1) y > 3x. If \(x=1\) and \(y=4\) then the range=6-1=5<9 but if \(x=100\) then the range>9. Not sufficient.

(2) y > x > 3. If \(x=4\) and \(y=5\) then the range=6-3=3<9 but if \(x=100\) then the range>9. Not sufficient.

(1)+(2) From \(x > 3\) we have that the least value of \(x\) is 4, and from \(y > 3x=12\) we have that the least value of \(y\) is 13, hence the least value of the range is 13-3=10>9. Sufficient.

Answer: C.

cyberjadugar · Answer

Hi,

Range = Largest value - smallest value.

6, 3, y, 4, 5, and x, where x & y are integers

Using (1),
y>3x, if x=1, then y = 4, 5,..100....
in each case range can be 5, 6,....So, range is greater than 5. Insufficient.

Using (2),
y>x>3.
Minimum value of x = 4,
y=5,6,7... We can't say whether range is greater than 9.

Combining both statements;
 x_{min} = 4 
& since, y > 3x,  y_{min}=13, 
thus, 3, 4, 4, 5, 6, & 13 has range (13-3)=10, which is greater than 9
and on increasing x, range will also increase.

Thus, answer is (C),

Regards,

mcelroytutoring · Answer

Here is a visual that should help.

mvictor · Answer

pretty easy for a 700 level question...

1. x can be 1, and y can be 4 - so the answer is NO
x can be 4, and y can be 13 - so the answer is YES.
1 alone is insufficient. A and D are out.

2. y>x>3.
x can be 4, y =5 - answer is no
x can be 4, y can be 20 - answer is YES.
2 alone is not sufficient. B is out.

1+2.
x>3
y>3x
minimum value for x is 4.
minimum value for y is 13
yes, the range is greater than 9.

sufficient.
answer is C.

JeffTargetTestPrep · Answer

Statement One Alone:

y > 3x

Statement one is not sufficient to answer the question. For example, if x = 0, y could be 1 and the range is 6 - 0 = 6, which is less than 9. However, if x = 10, y could be 31 and the range is 31 - 3 = 28, which is greater than 9.

Statement Two Alone:

y > x > 3

Statement two is not sufficient to answer the question. For example, if x = 4, y could be 5 and the range is 6 - 0 = 6, which is less than 9. However, if x = 14, y could be 15 and the range is 15 - 3 = 12, which is greater than 9.

Statements One and Two Together:

From the two statements, we know that x > 3 and y > 3x. So the smallest integer x can be is 4 and the smallest integer y can be is 3(4) + 1 = 13. Thus the smallest range of the integers is 13 - 3 = 10, which is greater 9. Since 10 is the smallest range, any other range of the integers will be greater than 10 and hence greater than 9.

Answer: C

arpitalewe · Answer

In the solution of these questions it is not asked to take minimum value and x and y can take any numbers so why we have solved this by taking minimum values

Gladiator59 · Answer

Hi  arpitalewe ,

Welcome to the GMAT Club!

So the logic behind trying to take the minimum permissible values for x and y is: we want to see if the minimum permissible value of y is such that range of the given set is greater than 9.  If for minimum value this condition holds then for all other values it will hold as well.

Hope this solves your doubt.

Let me know if you need further clarification or if the above solutions make sense with the above logic.

Regards,
Gladi

Salsanousi · Answer

Statement 1)

y > 3x

if x = 1 then y must be at least 4 but we cannot tell any further. 6-1 = 5 > 9 no.

If x = 5 y must be at least 16. 16 - 3 = 13 > 9 yes

Insufficient.

Statement 2)

y > x > 3 we can try the x = 4 and y = 5 we get an answer 6-3 = 3 > 9 no.

Try x = 4 y = 16, 16-3 = 13 > 9 yes.

Insufficient.

Now combine (1 and 2)

If x = 4 then y at least 13 (given that we took the minimum possible value for x)

13 - 3 = 10 > 9

Try x = 10 then y at least 31

31 - 3 = 28 > 9

Sufficient. Answer choice C

arpitalewe  check the above solution it might help.

Also as  Gladiator59  explained that the logic is to test if the minimum value satisfies the condition (range > 9) then the maximum will satisfy it too since y > 3x

Posted from my mobile device

Rishbha · Answer

Hello Bunuel,

In no explaination i see anyone considering x or y to be negative. In quesion it is mentioned they are integers, so will be right to consider negative values? Am i missing somethinghere? 
Also i assumed all the integers would be distinct, but unless stated , we can consider that integers are repeating, something i missed.

Thank you in advance for answering

Bunuel · Answer

(2) says that y > x > 3, so neither of them can be negative.

anonymous19 · Answer

I have one small doubt:

Doubt statement:  How do we know that x and y are integers since there is no mention of their nature. As per GMAT, unless not mentioned or derived from the available information, all numbers are real numbers. So, does it means that in a range, all values in the list must be the same type?

CEdward · Answer

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

3,4,5,6,x,y

Suppose y is the largest, then the question is asking whether y - 3 > 9 or y > 12?

(1) y > 3x
Let's say x = 3 ---> y > 9 so y = 10,11,12,13 are all valid
Insufficient
(2) y > x > 3
y = 5 --> R = 3
y = 10000000 --> R > 9
Insufficient

C: x = 4 at minimum so y > 3(4) ---> y > 12 at minimum

C

anonymous19  It states explicitly that x and y are integers. One should never assume indeed and your suspicion that they are all of the same type is fair. I don't recall ever seeing too many questions on here that mix types (unless otherwise stated)

adityaganjoo · Answer

Statement 1: y > 3x Let us say, x = -5000, then y> -15000; Say, y = -1000 Range: 6 - (-5000) > 9 However, if x is 0, then y> 3(0) or y>0; Say, y=1; Range: 6-0 = 6<9; So, (1) is unsufficient Statement 2: 3 9 Therefore, (2) is insufficient Combining (1) and (2): 33x Say, x=4 (as low within the constraints as possible) Therefore, y>12 Say, y=13 (as low within the constraints as possible) Range = 13-3 = 10 > 9 Any integer value of x > 4 would yield larger y and therefore, a range even larger than 9 Therefore, (C)

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=JRCVjdEiUwo Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

vrinda6 · Answer

Bunuel, I had a question in this solution- Doesn't this allow for multiple values of x and y?

Why are we only consdering the min value of x and y?

Bunuel · Answer

The solution is not saying that x and y have only one possible value. There are indeed multiple possible values.

The minimum values are considered because they give the  smallest possible range . From the two statements together, x must be at least 4, so y must be greater than 12, meaning y must be at least 13. Thus, even in the smallest possible case, the range is 13 - 3 = 10, which is already greater than 9.

So for any larger possible values of x and y, the range will still be  greater than 9 .

Is the range of the integers 6, 3, y, 4, 5, and x greater

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Is the range of the integers 6, 3, y, 4, 5, and x greater

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