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Math Expert V
Joined: 02 Sep 2009
Posts: 58312
10 distinct integers are arranged in ascending order. The range of the  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 67% (02:25) correct 33% (02:12) wrong based on 124 sessions

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10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range of the 10 numbers?

A. 25
B. 27
C. 30
D. 52
E. 55

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Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1686
Location: India
10 distinct integers are arranged in ascending order. The range of the  [#permalink]

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1
Positions: 1 2 3 4 5 6 7 8 9 10
Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b
y - x = 25
Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.
b - a = 30 --> b = 30 + a
In order to increase the range, we have to maximize the value of 'b'.
'b' can be maximized by taking the max value of 'a'.
From the assumed values, maximum value of 'a' can be 22.
Therefore, b = 30 + 22 = 52
Range = 52 - 0 = 52

Intern  Joined: 03 Mar 2014
Posts: 5
Re: 10 distinct integers are arranged in ascending order. The range of the  [#permalink]

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1
S7-S1 = 25
S10-S4 = 30
S1 = s7 -25
s10 = s4 + 30
S10 - s1 = s4 - s7 + 55 maximum range when s4 - s7 is minimum since s7 > s4, the min. value can be 3 as these are distinct
Manager  B
Joined: 01 Jul 2010
Posts: 59
Location: India
GMAT 1: 660 Q43 V38 GPA: 3.4
Re: 10 distinct integers are arranged in ascending order. The range of the  [#permalink]

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x7-x1=25
x10-x4=30

Add the above 2 equation
We want to calculate x10 - x1

(x10 -x1)+x7-x4=55
As the integers are in ascending order
x7 is greater than x4 when the integers are both positive or negative
so x10-x1 cannot be 55 and it has to be less that 55
x7-x4 can be as small as 3 consider 47 for x7 and 44 for x4
The maximum range can be 52 and the answer is D
Math Expert V
Joined: 02 Aug 2009
Posts: 7952
Re: 10 distinct integers are arranged in ascending order. The range of the  [#permalink]

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2
Bunuel wrote:
10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range of the 10 numbers?

A. 25
B. 27
C. 30
D. 52
E. 55

Hi,

1) Through avail choices
-->since last 7s range is 30, the range of all 10 is >30.. A,B and C eliminated
--> The range has to be <55 since 55 would be the range if there were 7+7 numbers.. E eliminated
Only D is left

2) Calculation..
first 7s range = 25
last 7s range = 30..
there are 7+7-10=4 in common..
to get max range, give these COMMON integers, 4th-7th, consecutive values..
say the seq= x,-,-,x+22,x+23,x+24,x+25,-,-,x+22+30
so last number= x+52..
range= x+52-x=52..

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Manager  Joined: 24 May 2013
Posts: 78
10 distinct integers are arranged in ascending order. The range of the  [#permalink]

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___1-------2------3-----------4----------5----------6----------------7----------8---------9-----------10

1. x................................................................ x+25
2. x.......................(x+22)....(x+23)....(x+24)
3. x...........................y..............................................................................y+30
4. x......................y=x+22......................................................................x+22+30 =x+52

Hence the range can be 52.
D is the answer.
Current Student D
Joined: 12 Aug 2015
Posts: 2574
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: 10 distinct integers are arranged in ascending order. The range of the  [#permalink]

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1
hey Bunuel just to be clear here if repetition of digits was allowed => range would have been 55 max?
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Math Expert V
Joined: 02 Aug 2009
Posts: 7952
Re: 10 distinct integers are arranged in ascending order. The range of the  [#permalink]

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1
Chiragjordan wrote:
hey Bunuel just to be clear here if repetition of digits was allowed => range would have been 55 max?

hi Chiragjordan,
you are absolutely correct..
first number could be 1 next 26 and till 9th number all are 26 and 10 th is 56..
Range ofcourse is 55..
While replying to you thought of another Q on it, would post it..
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Re: 10 distinct integers are arranged in ascending order. The range of the  [#permalink]

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_________________ Re: 10 distinct integers are arranged in ascending order. The range of the   [#permalink] 30 Sep 2018, 16:30
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