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# If each term in the sum a1+a2+a3+...+an

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Current Student
Joined: 12 Aug 2015
Posts: 2617
Schools: Boston U '20 (M)
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If each term in the sum a1+a2+a3+...+an  [#permalink]

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25 Aug 2016, 13:49
5
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:27) correct 27% (01:57) wrong based on 88 sessions

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If each term in the sum a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?

A. 38
B. 39
C. 40
D. 41
E. 42

Give me an Algebraic Solution..!!! No Hit and trials

Note => This question is just for practise . After doing the above try this Official GMAT prep Question too -> if-each-term-in-the-sum-a1-a2-a3-an-is-either-7-or-93974.html

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Re: If each term in the sum a1+a2+a3+...+an  [#permalink]

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25 Aug 2016, 14:13
Min value of 'n' can be 10 i.e 4*22+6*12 => 22+22+22+22+2+2+2+2+2+2 = 100

Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options

(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits

Hence C.
Current Student
Joined: 12 Aug 2015
Posts: 2617
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If each term in the sum a1+a2+a3+...+an  [#permalink]

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25 Aug 2016, 14:24
Argo wrote:
Min value of 'n' can be 10 i.e 4*22+6*12 => 22+22+22+22+2+2+2+2+2+2 = 100

Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options

(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits

Hence C.

Great Solution
BUT since its not an algebraic solution NO KUDOS for you

Good work though and try this using the algebraic method once .
One using the equations.

Regards
Stone Cold
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Re: If each term in the sum a1+a2+a3+...+an  [#permalink]

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27 Aug 2016, 01:45
1
stonecold wrote:
If each term in the sum a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?

A. 38
B. 39
C. 40
D. 41
E. 42

Give me an Algebraic Solution..!!! No Hit and trials

Note => This question is just for practise . After doing the above try this Official GMAT prep Question too -> if-each-term-in-the-sum-a1-a2-a3-an-is-either-7-or-93974.html

We are given 22k + 2k' = 100 .

Also, k+k' = n

In order to find the maximum value of n, we need to maximize the value of k' and minimize the value of k. Also, need to maintain the value of n an integer.

We cannot take k = 0, as we have atleast one 22 in the numbers.

So, lets say k=1, we will have 2k'=78 or k'=39

Therefore, n = 1+39=40

Hence, C
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Re: If each term in the sum a1+a2+a3+...+an  [#permalink]

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14 Dec 2016, 04:55
stonecold wrote:
If each term in the sum a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?

A. 38
B. 39
C. 40
D. 41
E. 42

Give me an Algebraic Solution..!!! No Hit and trials

Note => This question is just for practise . After doing the above try this Official GMAT prep Question too -> if-each-term-in-the-sum-a1-a2-a3-an-is-either-7-or-93974.html

$$2a + 22b = 100$$

$$a + 11b = 50$$

$$a_0 = 6$$

$$b_0 = 4$$

$$a = 6 + 11x$$

$$b = 4 - x$$

$$n = a + b = 10 + 10x = 10 (x + 1)$$

Our $$n$$ must be a multiple of $$10$$

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Re: If each term in the sum a1+a2+a3+...+an  [#permalink]

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15 Dec 2016, 02:52
As long as set consists of numbers "22" and "2", then it should contain at least 1 term of number "22", so since the sum is equal to 100, then 100-22=78, 78/2= 39 ===> 1ea. ( number 22) + 39 ea. ( number 22) = 40.
P.S. if we assume that this set contains more than one term of number "22" then, i.e. 100 - 2*22 = 66, 66/2=33 ==> 33+2 = 35 - less then any of the responses.
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Re: If each term in the sum a1+a2+a3+...+an  [#permalink]

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30 Nov 2018, 02:55
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Re: If each term in the sum a1+a2+a3+...+an   [#permalink] 30 Nov 2018, 02:55
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