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13 Nov 2023, 06:11
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C
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61% (02:14) correct
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A rectangular field with width x is marked with paint into 4ths and 7ths. In terms of x, what is the largest difference between any two consecutive 4th and 7th marks on this side of the field? (Assume there are no painted marks at the beginning or end of the field).
A. x/28
B. x/14
C. 3x/28
D. x/7
E. 5x/28
A. x/28
B. x/14
C. 3x/28
D. x/7
E. 5x/28
02 Mar 2025, 15:07
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Peterparker2
The 4th marks will be at: x/4, 2x/4, 3x/4 ..... and so on.
The 7th marks will be at: x/7, 2x/7, 3x/7 ..... and so on.
Now, taking LCM of 4 and 7 => 28, and expressing the 4th and 7th marks accordingly.
4x/28, 7x/28, 8x/28, 12x/28, 14x/28, 16x/28, 20x/28, 21x/28, 24x/28
The consecutive 4th and 7th marks are {[color=#005dc2]4x/28, 7x/28}, {12x/28, 14x/28}, and {20x/28, 21x/28}
The largest difference is between {4x/28, 7x/28} => 7x/28 - 4x/28 = 3x/28
Can you please recheck the source to make sure if in the answer choices \(x\) is in numerator?[/color]
General Discussion
13 Nov 2023, 07:57
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Arpansjain
I am sure you mean \(\frac{x}{28}\) and not \(\frac{1}{28x}\)
If I have to ease the question, I'll take x as 28.
4th mark would be at a distance of 28/4 or 7, so at 7,14,21
7th mark would be at a distance of 28/7 or 4, so at 4,8,12,16,20,24
combined paints will be at 4,7,8,12,14,16,20,21,24
The largest difference between two different consecutive markings will be at 7-4 or 24-21, that is 3.
substitute x as 28 in choices, C is \(\frac{3x}{28}=\frac{3*28}{28}=3\)
C
