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Kabir’s college is 12 miles from his hostel. He travels 6 miles from

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Kabir’s college is 12 miles from his hostel. He travels 6 miles from  [#permalink]

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New post 04 Oct 2018, 01:51
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Kabir’s college is 12 miles from his hostel. He travels 6 miles from the college to basketball practice, and then 4 miles to a computer class. If he is then D miles from hostel, what is the range of possible values for D?

(A) 2 ≤ D ≤ 10
(B) 2 ≤ D ≤ 16
(C) 2 ≤ D ≤ 12
(D) 2 ≤ D ≤ 22
(E) 4 ≤ D ≤ 20

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Re: Kabir’s college is 12 miles from his hostel. He travels 6 miles from  [#permalink]

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New post 04 Oct 2018, 03:51
Bunuel wrote:
Kabir’s college is 12 miles from his hostel. He travels 6 miles from the college to basketball practice, and then 4 miles to a computer class. If he is then D miles from home, what is the range of possible values for D?

(A) 2 ≤ D ≤ 10
(B) 2 ≤ D ≤ 16
(C) 2 ≤ D ≤ 12
(D) 2 ≤ D ≤ 22
(E) 4 ≤ D ≤ 20


Case 1: For shortest value of D, we may assume basketball practice and computer class on way back to home in that case distance travelled = 10 and distance left t be travelled = 12-10=2

Case 2: For Longest value of D, we may assume basketball practice and computer class on way away from home in that case distance travelled = 10 and distance left t be travelled = 12+10=22

i.e. 2≤ D ≤ 22

Answer: Option D
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Re: Kabir’s college is 12 miles from his hostel. He travels 6 miles from  [#permalink]

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New post 04 Oct 2018, 07:12
Bunuel wrote:
Kabir’s college is 12 miles from his hostel. He travels 6 miles from the college to basketball practice, and then 4 miles to a computer class. If he is then D miles from home, what is the range of possible values for D?

(A) 2 ≤ D ≤ 10
(B) 2 ≤ D ≤ 16
(C) 2 ≤ D ≤ 12
(D) 2 ≤ D ≤ 22
(E) 4 ≤ D ≤ 20

There can be 2 Scenarios :

Scenario - I
Attachment:
Scenario - I.png
Scenario - I.png [ 5.52 KiB | Viewed 799 times ]
The maximum distance in this case will be 22

Scenario - II
Attachment:
Scenario - II.png
Scenario - II.png [ 6.72 KiB | Viewed 802 times ]
The minimum distance in this case will be 2

Thus, the value of D must be between 2 and 22, Answer must be (D) 2 ≤ D ≤ 22
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Re: Kabir’s college is 12 miles from his hostel. He travels 6 miles from  [#permalink]

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New post 07 Oct 2018, 19:26
Bunuel wrote:
Kabir’s college is 12 miles from his hostel. He travels 6 miles from the college to basketball practice, and then 4 miles to a computer class. If he is then D miles from home, what is the range of possible values for D?

(A) 2 ≤ D ≤ 10
(B) 2 ≤ D ≤ 16
(C) 2 ≤ D ≤ 12
(D) 2 ≤ D ≤ 22
(E) 4 ≤ D ≤ 20


Let C = college, H = hostel (or home), B = basketball practice and P = computer class. If these places are all on the same line such that C, B, P and H are in this order, then D = PH = CH - CB - BP = 12 - 6 - 4 = 2 miles. This is the minimum value of D.

If we still assume C, H, P and H are on the same line, but the order is P, B, C and H, then D = PH = PB + BC + CH = 4 + 6 + 12 = 22 miles. This is the maximum value of D.

So 2 ≤ D ≤ 22.

Answer: D
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Re: Kabir’s college is 12 miles from his hostel. He travels 6 miles from  [#permalink]

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New post 16 Oct 2018, 01:41
Bunuel wrote:
Kabir’s college is 12 miles from his hostel. He travels 6 miles from the college to basketball practice, and then 4 miles to a computer class. If he is then D miles from home, what is the range of possible values for D?

(A) 2 ≤ D ≤ 10
(B) 2 ≤ D ≤ 16
(C) 2 ≤ D ≤ 12
(D) 2 ≤ D ≤ 22
(E) 4 ≤ D ≤ 20


Dear Moderator,
Small typo here it seems, in the latter part , the new term " Home " seems to be causing some confusion, perhaps it should be " Hostel". Hope you will look into this. Thank you.
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Re: Kabir’s college is 12 miles from his hostel. He travels 6 miles from  [#permalink]

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New post 16 Oct 2018, 01:58
stne wrote:
Bunuel wrote:
Kabir’s college is 12 miles from his hostel. He travels 6 miles from the college to basketball practice, and then 4 miles to a computer class. If he is then D miles from home, what is the range of possible values for D?

(A) 2 ≤ D ≤ 10
(B) 2 ≤ D ≤ 16
(C) 2 ≤ D ≤ 12
(D) 2 ≤ D ≤ 22
(E) 4 ≤ D ≤ 20


Dear Moderator,
Small typo here it seems, in the latter part , the new term " Home " seems to be causing some confusion, perhaps it should be " Hostel". Hope you will look into this. Thank you.


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Re: Kabir’s college is 12 miles from his hostel. He travels 6 miles from   [#permalink] 16 Oct 2018, 01:58
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