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04 Mar 2018, 15:17
Kudos
Bookmarks
Hi All,
This question has a lot of little facts to keep track of, but the math behind it isn't too tough.
We're told that there are integer shoe sizes (from 8 to 17) and each increase (from 8 to 9, 9 to 10, 10 to 11, etc.) increases the length of the shoe by 1/4 inch. Next, we're told that the largest shoe (size 17) is 20% longer than the smallest shoe (size 8). We're asked for the size of a SIZE 15 SHOE…
From size 8 to size 17, there are 9 "increases" of 1/4 inch.
9(1/4) = 2.25 inches
This 2.25 inches represents the 20% increase in length from size 8 to size 17, so we can determine the length of a size 8 shoe.
X = length of a size 8 shoe
.2X = 2.25
X = (2.25)(5)
X = 11.25
Size 8 = 11.25 inches
Size 17 = 13.5 inches
From here, we can either "count up" from Size 8 or "count down" from Size 17. Counting down will likely be easier and faster.
Size 17 = 13.5 - 2(1/4) = 13
Size 15 = 13 inches
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This question has a lot of little facts to keep track of, but the math behind it isn't too tough.
We're told that there are integer shoe sizes (from 8 to 17) and each increase (from 8 to 9, 9 to 10, 10 to 11, etc.) increases the length of the shoe by 1/4 inch. Next, we're told that the largest shoe (size 17) is 20% longer than the smallest shoe (size 8). We're asked for the size of a SIZE 15 SHOE…
From size 8 to size 17, there are 9 "increases" of 1/4 inch.
9(1/4) = 2.25 inches
This 2.25 inches represents the 20% increase in length from size 8 to size 17, so we can determine the length of a size 8 shoe.
X = length of a size 8 shoe
.2X = 2.25
X = (2.25)(5)
X = 11.25
Size 8 = 11.25 inches
Size 17 = 13.5 inches
From here, we can either "count up" from Size 8 or "count down" from Size 17. Counting down will likely be easier and faster.
Size 17 = 13.5 - 2(1/4) = 13
Size 15 = 13 inches
Final Answer:
GMAT assassins aren't born, they're made,
Rich
22 Apr 2021, 09:57
Kudos
Bookmarks
Great question bringing in elements of an AP and algebra.
We have 10 shoe sizes from 8 to 17
Let the smallest shoe size (8) ——— X
Then there is a common difference between each consecutive shoe size = +(1/4)
The largest shoe size (17) will have ———- +9 * (1/4) added to the smallest shoe size
“Largest shoe size is 20% larger than smallest shoe size”
X + (9) (1/4) = (120%) (X)
X + (9/4) = (6/5) (X)
(9/4) = (X / 5)
X = 45/4
The shoe size given by integer 15 will be the 8th term in the arithmetic progression/evenly spaced set ———-> size = X + (7) (1/4)
Substitute in the value of X
(45/4) + (7/4) = (52/4) = 13
(E)
13 is the answer
Posted from my mobile device
We have 10 shoe sizes from 8 to 17
Let the smallest shoe size (8) ——— X
Then there is a common difference between each consecutive shoe size = +(1/4)
The largest shoe size (17) will have ———- +9 * (1/4) added to the smallest shoe size
“Largest shoe size is 20% larger than smallest shoe size”
X + (9) (1/4) = (120%) (X)
X + (9/4) = (6/5) (X)
(9/4) = (X / 5)
X = 45/4
The shoe size given by integer 15 will be the 8th term in the arithmetic progression/evenly spaced set ———-> size = X + (7) (1/4)
Substitute in the value of X
(45/4) + (7/4) = (52/4) = 13
(E)
13 is the answer
Posted from my mobile device
10 Sep 2024, 09:50
Kudos
Bookmarks
from size 8 to size 17 , there are 10 elements.
Let , size 8 = x
size 17 = x + 9/4
x+9/4 = x (1 +1/5)
x= 45/4
The no 15 shoe will be the (15 - 8 ) + 1 = 8th term and hence x + (8-1)/4 = (45+7)/ 4 = 13
E is the answer.
Let , size 8 = x
size 17 = x + 9/4
x+9/4 = x (1 +1/5)
x= 45/4
The no 15 shoe will be the (15 - 8 ) + 1 = 8th term and hence x + (8-1)/4 = (45+7)/ 4 = 13
E is the answer.
