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# Mani saves money in a jar at home for six months. The first month he

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Math Expert
Joined: 02 Sep 2009
Posts: 45498
Mani saves money in a jar at home for six months. The first month he [#permalink]

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25 Apr 2018, 21:51
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83% (02:06) correct 17% (02:42) wrong based on 30 sessions

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Mani saves money in a jar at home for six months. The first month he saves S dollars. Each month thereafter, Mani saves 1/2 of what he has saved the previous month. If Mani’s total savings at the end of the six months is $393.75, how much money does he save the sixth month? (A)$6.25
(B) $7.50 (C)$12.50
(D) $18.75 (E)$25.00

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Re: Mani saves money in a jar at home for six months. The first month he [#permalink]

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25 Apr 2018, 22:34
Bunuel wrote:
Mani saves money in a jar at home for six months. The first month he saves S dollars. Each month thereafter, Mani saves 1/2 of what he has saved the previous month. If Mani’s total savings at the end of the six months is $393.75, how much money does he save the sixth month? (A)$6.25
(B) $7.50 (C)$12.50
(D) $18.75 (E)$25.00

$$S+\frac{1}{2}S+\frac{1}{4}S+\frac{1}{8}S+\frac{1}{16}S+\frac{1}{32}S=393\frac{3}{4}$$

$$\frac{63}{32}S=\frac{1575}{4}$$

Note that $$1575*4=6300$$.

So, $$S=200$$.

We are asked to find the amount of money he saved the sixth month. That is $$\frac{200}{32}=6.25$$

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Re: Mani saves money in a jar at home for six months. The first month he [#permalink]

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25 Apr 2018, 22:42
Bunuel wrote:
Mani saves money in a jar at home for six months. The first month he saves S dollars. Each month thereafter, Mani saves 1/2 of what he has saved the previous month. If Mani’s total savings at the end of the six months is $393.75, how much money does he save the sixth month? (A)$6.25
(B) $7.50 (C)$12.50
(D) $18.75 (E)$25.00

he saves S in first month thereafter 1/2 of what he saved the previous month. so for six months

S+$$\frac{1}{2}$$S+$$\frac{1}{4}$$S+$$\frac{1}{8}$$S+$$\frac{1}{16}$$S+$$\frac{1}{32}$$S = 393.75

simplify we get , $$\frac{63}{32}$$S= 393.75

we are asked to find $$\frac{1}{32}$$S (Sixth month saving)

So $$\frac{S}{32}$$=$$\frac{393.75*32}{63*32}$$S= 6.25
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Re: Mani saves money in a jar at home for six months. The first month he [#permalink]

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13 May 2018, 10:14
Above question can be solved by two methods

I) S+ S/2 + S/4 +S/8+ S/16+ S/32= 393.75

Calculate S and then S/32 for last value

II) by calculating sum of gp with r=1/2

S((1/2)^6-1)/ (1/2-1)=393.75

63S/32=393.75

S=6.25*32

Last term =S*(1/2)^6=6.25

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Re: Mani saves money in a jar at home for six months. The first month he [#permalink]

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13 May 2018, 12:44
Bunuel wrote:
Mani saves money in a jar at home for six months. The first month he saves S dollars. Each month thereafter, Mani saves 1/2 of what he has saved the previous month. If Mani’s total savings at the end of the six months is $393.75, how much money does he save the sixth month? (A)$6.25
(B) $7.50 (C)$12.50
(D) $18.75 (E)$25.00

Since Mani's total savings at the end of six months is $393.75 and he was able to save half of what he had saved the previous month, it is also safe to assume that the savings double each month(if we begin calculating from the last month) Let's consider Option A(6.25) as the amount he would have saved in the 6th month. So, the 5th month he would have saved xx.50 and every month after that he would have saved xx.00. The sum would be xxx.75 and could be our answer. Let's consider Option D(18.75). So in the 5th month, he would save xx.50 and there after every month he would save xx.00. The sum would be xxx.25. We can eliminate Option B,C, and E for similar reasons Therefore, Option A($6.25) is the amount Mani saves in the sixth month.
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Re: Mani saves money in a jar at home for six months. The first month he   [#permalink] 13 May 2018, 12:44
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