A Question from Manhattan Gmat - Advanced GMAT Quant

[maryam177]

Hi, this question is from Manhattan Gmat - Advanced GMAT Quant:

A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1-mile stretch. Between the two black lines, they will paint across the road a red line at each third of a mile, a white line at each fifth of a mile, and a blue line at each eighth of a mile. What is the smallest distance (in miles) between any of the painted lines on this stretch of highway?

(A) 0
(B) 1/120
(C) 1/60
(D) 1/40
(E) 1/30

I don't understand this part of the explanation :

The smallest distance between two marks is 75 - 72 = 3 or 48 - 45 = 3. This equates to 3/120, or 1/40 miles.

My question is that why is the smallest distance 3 out of 120 and not 1 out of 120? Why do we subtract 72 from 75?

[RonPurewal]

Hi, this question is from Manhattan Gmat - Advanced GMAT Quant:

A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1-mile stretch. Between the two black lines, they will paint across the road a red line at each third of a mile, a white line at each fifth of a mile, and a blue line at each eighth of a mile. What is the smallest distance (in miles) between any of the painted lines on this stretch of highway?

(A) 0
(B) 1/120
(C) 1/60
(D) 1/40
(E) 1/30

I don't understand this part of the explanation :

The smallest distance between two marks is 75 - 72 = 3 or 48 - 45 = 3. This equates to 3/120, or 1/40 miles.

My question is that why is the smallest distance 3 out of 120 and not 1 out of 120? Why do we subtract 72 from 75?

because there's not a line every 1/120 of a mile.

to do this problem, you have to make a list of where the marks actually are"”and then just find the elements of the list that are closest to each other.

the fifths are at 1/5, 2/5, 3/5, and 4/5. in terms of the common denominator, that's 24/120, 48/120, 72/120, and 96/120.

the eighths are at 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, and 7/8. in terms of the common denominator, that's 15/120, 30/120, 45/120, 60/120, 75/120, 90/120, and 105/120.

the thirds are at 1/3 and 2/3. in terms of the common denominator, that's 40/120 and 80/120.

the closest you'll get between any two of these is 3/120. you can't get within 1/120 because ... well, because you can't.

[maryam177]

[quote="RonPurewal"][quote="maryam177"]Hi, this question is from Manhattan Gmat - Advanced GMAT Quant:

A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1-mile stretch. Between the two black lines, they will paint across the road a red line at each third of a mile, a white line at each fifth of a mile, and a blue line at each eighth of a mile. What is the smallest distance (in miles) between any of the painted lines on this stretch of highway?

(A) 0
(B) 1/120
(C) 1/60
(D) 1/40
(E) 1/30

I don't understand this part of the explanation :

The smallest distance between two marks is 75 - 72 = 3 or 48 - 45 = 3. This equates to 3/120, or 1/40 miles.

My question is that why is the smallest distance 3 out of 120 and not 1 out of 120? Why do we subtract 72 from 75?[/quote]

because there's not a line every 1/120 of a mile.

to do this problem, you have to [b]make a list[/b] of where the marks actually are"”and then just find the elements of the list that are closest to each other.

the fifths are at 1/5, 2/5, 3/5, and 4/5. in terms of the common denominator, that's 24/120, 48/120, 72/120, and 96/120.

the eighths are at 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, and 7/8. in terms of the common denominator, that's 15/120, 30/120, 45/120, 60/120, 75/120, 90/120, and 105/120.

the thirds are at 1/3 and 2/3. in terms of the common denominator, that's 40/120 and 80/120.

the closest you'll get between any two of these is 3/120. you can't get within 1/120 because ... well, because you can't.[/quote]



Thank you Ron

[jnelson0612]

Thanks!