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Smith bought a set of six bottles of different sizes at a total price
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10 Jan 2024, 00:17
10 Jan 2024, 00:17
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Question Stats:
80% (02:04) correct
20% (02:35) wrong based on 5 sessions
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Smith bought a set of six bottles of different sizes at a total price of $75. The price of each bottle is $d more than the next one below it in size. If the price of each bottle is an integer, what could be the price, in dollars, of the smallest bottle?
Indicate all possible values.
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
(F) $8
(G) $10
Indicate all possible values.
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
(F) $8
(G) $10
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Free Materials for the GRE General Exam - Where to get it!!
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Re: Smith bought a set of six bottles of different sizes at a total price
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01 Feb 2024, 03:53
01 Feb 2024, 03:53
1
The answers are E and G.
Since the difference between the price of each bottle is constant ($d), we are dealing an arithmetic progression here.
Let the price of the smallest bottle = s
--> Price of the other bottles --> s + d, s + 2d, s + 3d, s + 4d, s + 5d
--> Total --> $75 = s + (s + d) + (s + 2d) + (s + 3d) + (s + 4d) + (s + 5d)
--> 6s + 15d = 75
Check values for s:
If s = 1, 6*1 + 15d = 75 --> 15d = 69 (not possible)
If s = 2, 6*2 + 15d = 75 --> 15d = 63 (not possible)
If s = 3, 6*3 + 15d = 75 --> 15d = 57 (not possible)
If s = 4, 6*4 + 15d = 75 --> 15d = 51 (not possible)
If s = 5, 6*5 + 15d = 75 --> 15d = 45 (possible)
If s = 8, 6*8 + 15d = 75 --> 15d = 27 (not possible)
If s = 10, 6*10 + 15d = 75 --> 15d = 15 (possible)
Since the difference between the price of each bottle is constant ($d), we are dealing an arithmetic progression here.
Let the price of the smallest bottle = s
--> Price of the other bottles --> s + d, s + 2d, s + 3d, s + 4d, s + 5d
--> Total --> $75 = s + (s + d) + (s + 2d) + (s + 3d) + (s + 4d) + (s + 5d)
--> 6s + 15d = 75
Check values for s:
If s = 1, 6*1 + 15d = 75 --> 15d = 69 (not possible)
If s = 2, 6*2 + 15d = 75 --> 15d = 63 (not possible)
If s = 3, 6*3 + 15d = 75 --> 15d = 57 (not possible)
If s = 4, 6*4 + 15d = 75 --> 15d = 51 (not possible)
If s = 5, 6*5 + 15d = 75 --> 15d = 45 (possible)
If s = 8, 6*8 + 15d = 75 --> 15d = 27 (not possible)
If s = 10, 6*10 + 15d = 75 --> 15d = 15 (possible)
gmatclubot
Re: Smith bought a set of six bottles of different sizes at a total price [#permalink]
01 Feb 2024, 03:53
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