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Let a1, a2, ... , a52 be positive integers such that

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Manager
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Joined: 01 Nov 2017
Posts: 67
Location: India
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Let a1, a2, ... , a52 be positive integers such that  [#permalink]

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New post 26 Feb 2019, 23:36
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

19% (02:43) correct 81% (02:09) wrong based on 27 sessions

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Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ... < a52. Suppose, their arithmetic mean is one less than the arithmetic mean of a2, a3, ..., a52. If a52 = 100, then the largest possible value of a1 is

(A) 20
(B) 23
(C) 48
(D) 45
(E) 22
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B
Joined: 29 Nov 2016
Posts: 174
Location: India
GMAT 1: 750 Q50 V42
Re: Let a1, a2, ... , a52 be positive integers such that  [#permalink]

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New post 10 Mar 2019, 05:32
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1
Let (a2+a3....a52 )/51=M2
And (a1+a2.....a52)/52= M1
Now
M2-1=M1
Or M2=M1+1
Substituting M2 and M1
(a2+a3....a52)/51= (a1+a2.....a52)/52 +1
Or
(a2+a3....a52)*52= [(a1+a2.....a52)+52]*51
subtracting 51*[a1+a2....a52] from both sides
a2+a3+....a52=51a1+52*51
Or
(a2+a3.....a52)/51= a1+52
Or
M2=a1+52
Now can max value of a1 be 48? => NO because this will give M2 =100 and mean of numbers where a1<a2<100 can not be 100
Simillarly a1 can not be 45 as mean can not be 97.
a1 can be 20,23,22 but in order to maicimize the value of a1 it has to be 23.
Hence B.

Please press kudos if u like the solution. Thanks in advance.

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Re: Let a1, a2, ... , a52 be positive integers such that  [#permalink]

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New post 07 Mar 2019, 08:20
Hello!

I think this is a CAT question, a bit difficult than a real 600+ GMAT questions but still very interesting!

Can someone please provide an answer?

Kind regards!
GMAT Club Bot
Re: Let a1, a2, ... , a52 be positive integers such that   [#permalink] 07 Mar 2019, 08:20
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Let a1, a2, ... , a52 be positive integers such that

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