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# Jo and Blair take turns counting from 1 to one more than the last numb

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Math Expert
Joined: 02 Sep 2009
Posts: 59725
Jo and Blair take turns counting from 1 to one more than the last numb  [#permalink]

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20 Mar 2019, 04:48
00:00

Difficulty:

35% (medium)

Question Stats:

71% (02:02) correct 29% (01:47) wrong based on 38 sessions

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Jo and Blair take turns counting from 1 to one more than the last number said by the other person. Jo starts by saying 1, so Blair follows by saying 1, 2. Jo then says 1, 2, 3, and so on. What is the 53rd number said?

(A) 2
(B) 3
(C) 5
(D) 6
(E) 8

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Re: Jo and Blair take turns counting from 1 to one more than the last numb  [#permalink]

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20 Mar 2019, 05:08
1
Jo says 1 = 1
Blair says 1,2= 2
Jo says 1,2,3= 3
Similarly 1+2+3+4+5+6+7+8+9= 45 numbers covered
Now Blair says 10 numbers 1 to 10 then total numbers told will be 55 numbers,where 53rd number will be 8
OA:(E)

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Re: Jo and Blair take turns counting from 1 to one more than the last numb  [#permalink]

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20 Mar 2019, 07:28
Bunuel wrote:
Jo and Blair take turns counting from 1 to one more than the last number said by the other person. Jo starts by saying 1, so Blair follows by saying 1, 2. Jo then says 1, 2, 3, and so on. What is the 53rd number said?

(A) 2
(B) 3
(C) 5
(D) 6
(E) 8

Only feasible method I found to solve this was to write the series
IMO E ; 8 will be the 53rd no
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Re: Jo and Blair take turns counting from 1 to one more than the last numb  [#permalink]

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22 Mar 2019, 05:15
Bunel , do you have explanation?
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Re: Jo and Blair take turns counting from 1 to one more than the last numb  [#permalink]

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22 Mar 2019, 05:27
2
Bunuel wrote:
Jo and Blair take turns counting from 1 to one more than the last number said by the other person. Jo starts by saying 1, so Blair follows by saying 1, 2. Jo then says 1, 2, 3, and so on. What is the 53rd number said?

(A) 2
(B) 3
(C) 5
(D) 6
(E) 8

Doesn't matter who is saying the numbers, we just need to know the 53rd number said.

1 (1 number said)

1, 2 (2 numbers said)

1, 2, 3 (3 numbers said)

1, 2, 3, 4 (4 numbers said)

These numbers said (1 + 2 + 3 + 4 + ...) should add up to 53. We know that (1 + 2+ 3 + ... + 9 = 9*10/2 = 45).

So 1, 2, 3, ... 9 (9 numbers said)

These all will add up to 45 numbers. We need to say another 8 numbers now. Next will be

1, 2, 3, 4, ...8 (STOP - 53rd number), 9 , 10

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Re: Jo and Blair take turns counting from 1 to one more than the last numb  [#permalink]

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22 Mar 2019, 05:35
Bunuel wrote:
Jo and Blair take turns counting from 1 to one more than the last number said by the other person. Jo starts by saying 1, so Blair follows by saying 1, 2. Jo then says 1, 2, 3, and so on. What is the 53rd number said?

(A) 2
(B) 3
(C) 5
(D) 6
(E) 8

Doesn't matter who is saying the numbers, we just need to know the 53rd number said.

1 (1 number said)

1, 2 (2 numbers said)

1, 2, 3 (3 numbers said)

1, 2, 3, 4 (4 numbers said)

These numbers said (1 + 2 + 3 + 4 + ...) should add up to 53. We know that (1 + 2+ 3 + ... + 9 = 9*10/2 = 45).

So 1, 2, 3, ... 9 (9 numbers said)

These all will add up to 45 numbers. We need to say another 8 numbers now. Next will be

1, 2, 3, 4, ...8 (STOP - 53rd number), 9 , 10

it is very clear. kudos to you.
Thank you
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Re: Jo and Blair take turns counting from 1 to one more than the last numb  [#permalink]

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24 Mar 2019, 18:33
Bunuel wrote:
Jo and Blair take turns counting from 1 to one more than the last number said by the other person. Jo starts by saying 1, so Blair follows by saying 1, 2. Jo then says 1, 2, 3, and so on. What is the 53rd number said?

(A) 2
(B) 3
(C) 5
(D) 6
(E) 8

We see that the number of numbers Jo and Blair are each, alternatively, saying is 1, 2, 3, 4, 5, etc. Therefore, we want to add up these numbers to get the sum that is closest to 53 as possible.
Since 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 and the number of numbers Jo says is always odd, we see that Jo says 9 as the 45th number overall. Then, Blair says 1 as the 46th number, 2 the 47th number, …, 8 as the 53rd number.

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Re: Jo and Blair take turns counting from 1 to one more than the last numb   [#permalink] 24 Mar 2019, 18:33
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