Set Q contains 20 positive integer values. The smallest value in Set Q

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Set Q contains 20 positive integer values. The smallest value in Set Q is a single-digit value and the largest value in Set Q is a three-digit value. What are the possible values for the range of Set Q?

I. 90
II. 100
III. 995

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

I. 90
II. 100
III. 995

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

harsh61998 · Answer

IMO D.

Case 1: Range is 90. It is not possible because the lowest possible value is a single digit number, for example 9 and the largest possible number is a 3-digit number for example 100. Therefore the minimum range of the numbers is 91 (100 - 9).
We can safely eliminate options  A and E

Case 2: Range is 100. This is possible.
Let the lowest possible number be 1 and the largest possible number be 101. Therefore, the range is 100 (101 - 1).

Case 3: Range is 995. This is also possible.
Let the lowest possible number be 4 and the largest possible number 999. Therefore, the range is 995 (999 - 4).

Therefore, II and III both are sufficient.

Answer:  D

kawal27 · Answer

RANGE = largest - smallest in given set

smallest 3 digit positive integer 100 and largest is 999
smallest single digit positive integer is 1 and largest is 9

I. 90 if we take smallest 3 digit integer - largest single digit (100-9) which is 91 , not possible
II. 100 ( 101-1) possible
III. 995 (999-4) possible

ANSWER:D
“All our dreams can come true, if we have the courage to pursue them.”

yashikaaggarwal · Answer

The maximum range is when the single digit number is biggest = 9, and three digit number is least = 100
That's : 100-9 = 91

The minimum range is when the single digit number is least = 1, and three digit number is greatest = 999
That's : 999-1 = 998

The range lies in between 91 ≥ Range ≥ 998
Which satisfies both 2&3 value

Answer is D

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GMATWhizTeam · Answer

Solution 
 • Set Q contains 20  positive integers 
 o The smallest of which is a single – digit value.
o The largest of which is a three-digit value. 
• We need to find the possible range of Set Q.
• Now, the minimum range of Q = The smallest three-digit positive integer – The largest single-digit positive integer.
   ⟹ \space the \space minimum \space range \space of \space Q = 100 – 9 = 91 …….Eq.(i)  
• Also, the maximum range of Q = The largest three-digit positive integer – The smallest single-digit positive integer.
   ⟹ \space the \space maximum \space range \space of \space Q = 999 – 1 = 998 ……….Eq.(ii)  
• On combining Eq.(i) and Eq.(ii), we get,
 o  91 ≤ Range \space of \space Set \space Q ≤ 998  
• Hence,100 and 995 can be possible values for the range of set, however 90 cannot be. 
Thus, the correct answer is  Option D.

rajatchopra1994 · Answer

Explanation:

Maximum possible range (999 is largest, 1 is lowest): 999 - 1 = 998

Minimum possible range (100 is largest, 9 is lowest): 100 - 9 = 91

100, 995 comes under range from 91 to 998

IMO-D

exc4libur · Answer

Q = {20 positive integer values}
a = {1 to 9}
tn = {100 to 999}
max rng = 999-1 = 998
min rng = 100-9 = 91

Ans (D)

AnirudhaS · Answer

Given, all psoitive, all integers, smallest(1 - 9), largest (100 - 999)

I. 90
Not possible, the lowest range would be = 100-9=91

II. 100
Possible in various scenarios, one such = 105-5 = 100

III. 995
Possible in various scenarios, one such = 999-4 = 995

Answer:  D

sambitspm · Answer

Kindly see the attachment. As only possible answers for range are required, you can start by assuming smallest number - unit digit.
IMO D

suchita2409 · Answer

D

90 is not possible.

least 3 digit is 100-9=91
minimum range is 91.

Other 2 values are possible.
109 - 9 = 100.
Other pairs could also give us 100.

995= 999-4

Other pairs could also give us 995.

So 2 & 3

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monikakumar · Answer

Set Q contains 20 positive integer values. The smallest value in Set Q is a single-digit value and the largest value in Set Q is a three-digit value. What are the possible values for the range of Set Q?

I. 90
II. 100
III. 995

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

I. 90
II. 100
III. 995

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

single-digit = 1 to 9
3-digit = 100 to 999

min = 100-9 = 91
max = 999-1=998

so, 100, 995 are in the range
Ans D

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Set Q contains 20 positive integer values. The smallest value in Set Q

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Set Q contains 20 positive integer values. The smallest value in Set Q

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