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11 Feb 2020, 02:30
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D
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Difficulty:
25%
(medium)
Question Stats:
76% (01:31) correct
24%
(01:24)
wrong
based on 116
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A parent established a college fund for his daughter. Each year the parent made a contribution to the fund, and each year he increased his contribution by a constant amount. If he made a contribution of $800 in the first year, by what amount did the parent increase his contribution to the fund each year?
(1) The parent's contribution to the fund in the 18th year was $7600.
(2) The parent's contribution to the fund in the 7th year was twice what it was in the 3rd year.
(1) The parent's contribution to the fund in the 18th year was $7600.
(2) The parent's contribution to the fund in the 7th year was twice what it was in the 3rd year.
11 Feb 2020, 02:46
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for all years we have
1st= 800
2nd= 800+x
so on till 18th year ; 800+17x
#1
The parent's contribution to the fund in the 18th year was $7600.
800+17x=7600
x=400
sufficient
#2
The parent's contribution to the fund in the 7th year was twice what it was in the 3rd year.
800+6x=2*(800+2x)
x=400
sufficient
IMO D
1st= 800
2nd= 800+x
so on till 18th year ; 800+17x
#1
The parent's contribution to the fund in the 18th year was $7600.
800+17x=7600
x=400
sufficient
#2
The parent's contribution to the fund in the 7th year was twice what it was in the 3rd year.
800+6x=2*(800+2x)
x=400
sufficient
IMO D
Bunuel
A parent established a college fund for his daughter. Each year the parent made a contribution to the fund, and each year he increased his contribution by a constant amount. If he made a contribution of $800 in the first year, by what amount did the parent increase his contribution to the fund each year?
(1) The parent's contribution to the fund in the 18th year was $7600.
(2) The parent's contribution to the fund in the 7th year was twice what it was in the 3rd year.
(1) The parent's contribution to the fund in the 18th year was $7600.
(2) The parent's contribution to the fund in the 7th year was twice what it was in the 3rd year.
12 Feb 2020, 23:29
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Bunuel
A parent established a college fund for his daughter. Each year the parent made a contribution to the fund, and each year he increased his contribution by a constant amount. If he made a contribution of $800 in the first year, by what amount did the parent increase his contribution to the fund each year?
(1) The parent's contribution to the fund in the 18th year was $7600.
(2) The parent's contribution to the fund in the 7th year was twice what it was in the 3rd year.
(1) The parent's contribution to the fund in the 18th year was $7600.
(2) The parent's contribution to the fund in the 7th year was twice what it was in the 3rd year.
Solution
Step 1: Analyse Question Stem
- • The contribution in first year is $800.
• Each year contribution is increased by a certain amount (let’s say $d).
- o Thus, the contribution in each successive years will be: $800, $(800+d), $(800+2d) …. and so on.
- So, we can see that contribution in each year is in A.P. (arithmetic progression).
So, contribution in the nth year will be = 800 + (n-1) *d
- o Or say, the common difference of A.P. formed by the contributions done in each year.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The parent's contribution to the fund in the 18th year was $7600.
- • According to this statement, \(800 + (18-1) *d = 7600\)
Hence, statement 1 is sufficient and we can eliminate answer options B, C and E
Statement 2: The parent's contribution to the fund in the 7th year was twice what it was in the 3rd year
- • According to this statement, \(2*(800 + (3-1) *d) = 800 +(7-1) *d\)
Hence, statement 2 is also sufficient.
Thus, the correct answer is Option D.
