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A certain clock rings two notes at quarter past the hour, four notes

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A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 27 Oct 2019, 21:39
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

51% (01:57) correct 49% (01:54) wrong based on 39 sessions

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A certain clock rings two notes at quarter past the hour, four notes at half past, and six notes at three-quarters past. On the hour, it rings eight notes plus an additional number of notes equal to whatever hour it is. How many notes will the clock ring from 1:00 p.m. through 5:00 p.m., including the rings at 1:00 and 5:00?

(A) 87
(B) 95
(C) 102
(D) 103
(E) 115

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Re: A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 27 Oct 2019, 21:58
( 20 x 4 ) + ( 1 + 2 + 3 + 4 + 5 ) = 95.

B

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Re: A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 27 Oct 2019, 22:03
1
Lets first get the count for 15 mins,30 mins,45 mins ring.

1-2 2 + 4 + 6 =12
2-3 =12
3-4 =12
4-5 =12

Total 48

Now lets calculate at each hour

1 8 + 1 = 9
2 = 10
3 = 11
4 = 12
5 = 13

= 55

So total rings = 48 + 55 = 103

hence D

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Re: A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 27 Oct 2019, 23:48
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A certain clock rings two notes at quarter past the hour, four notes at half past, and six notes at three-quarters past. On the hour, it rings eight notes plus an additional number of notes equal to whatever hour it is. How many notes will the clock ring from 1:00 p.m. through 5:00 p.m., including the rings at 1:00 and 5:00?

(A) 87
(B) 95
(C) 102
(D) 103
(E) 115

As per the question at every hour eight notes ring plus additional notes for the number of hour it rings eight notes for. For every 15minutes past the hour 2 notes, 30 minutes past the hour 4 notes and 45 minutes 6 minutes. Refer snapshot below.
Attachment:
File comment: Clock notes
Clock notes.png
Clock notes.png [ 37.6 KiB | Viewed 519 times ]

Since only notes for hour starting 5pm are counted, no notes are to be considered past it.

Answer D.
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Re: A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 27 Oct 2019, 23:59
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OA:D
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Re: A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 28 Oct 2019, 00:39
1
A certain clock rings two notes at quarter past the hour, four notes at half past, and six notes at three-quarters past. On the hour, it rings eight notes plus an additional number of notes equal to whatever hour it is. How many notes will the clock ring from 1:00 p.m. through 5:00 p.m., including the rings at 1:00 and 5:00?

2(4)+
4(4)+
6(4)+
8(5)+1+2+3+4+5
=8+16+24+40+15
=103

(A) 87
(B) 95
(C) 102
(D) 103
(E) 115

Therefore, D
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Re: A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 28 Oct 2019, 02:57
1
for following mins the clock rings
15-2
30-4
45-6
i,e 12 times in between hours
and
for every hour 8+ ( count of hr hand)
so from 1 PM to 5 PM
we have
4*12+8*5+(1+2+3+4+5) = 48+40+15 ; 103
IMO D

A certain clock rings two notes at quarter past the hour, four notes at half past, and six notes at three-quarters past. On the hour, it rings eight notes plus an additional number of notes equal to whatever hour it is. How many notes will the clock ring from 1:00 p.m. through 5:00 p.m., including the rings at 1:00 and 5:00?

(A) 87
(B) 95
(C) 102
(D) 103
(E) 115
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Re: A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 28 Oct 2019, 03:07
1
—> From 01:00 to 02:00 —> (8+1)+ (2+4+6+8)+ 2 = 31 notes ( including 01:00 and 02:00)

—> from 02:00 to 03:00–> (2+4+6+8)+ 3= 23 (including 03:00)

—> from 03:00 to 04:00–> (2+4+6+8)+ 4= 24 (including 04:00)

—>from 04:00 to 05:00–> (2+4+6+8)+ 5= 25 (including 05:00)

In total, the clock will ring 31+23+24+25= 103 notes from 01:00 to 05:00 p.m.

The answer is D

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A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post Updated on: 02 Nov 2019, 14:07
Quote:
A certain clock rings two notes at quarter past the hour, four notes at half past, and six notes at three-quarters past. On the hour, it rings eight notes plus an additional number of notes equal to whatever hour it is. How many notes will the clock ring from 1:00 p.m. through 5:00 p.m., including the rings at 1:00 and 5:00?

(A) 87
(B) 95
(C) 102
(D) 103
(E) 115


1:00 = 8 + (1) = 9
1:00-2:00 = 2 + 4 + 6 + 8 + (2) = 22
2:00-3:00 = 2 + 4 + 6 + 8 + (3) = 23
3:00-4:00 = 2 + 4 + 6 + 8 + (4) = 24
4:00-5:00 = 2 + 4 + 6 + 8 + (5) = 25
Total = 103 notes

Answer (D)

Originally posted by exc4libur on 28 Oct 2019, 06:57.
Last edited by exc4libur on 02 Nov 2019, 14:07, edited 1 time in total.
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Re: A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 28 Oct 2019, 07:41
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4×2 + 4×4 + 4×6 + 9+10+11+12+13= 103

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A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post Updated on: 28 Oct 2019, 22:42
From 1pm to 5pm, we have five hours, since the clock will ring on the 1pm hour mark as well.

Total number of notes = 5*(no. notes on the quarter-hour past the hour mark + number of notes on half hour past the hour mark + number of notes on three quarters past the hour mark + no. of notes on the hour mark) + no. of rings on the 5pm hour mark + 1+2+3+4+5
=4*(2+4+6+8)+8+15
=80+8+15
=103.

The answer is option D.

Nice question. I got it wrong the first time.

Originally posted by eakabuah on 28 Oct 2019, 09:30.
Last edited by eakabuah on 28 Oct 2019, 22:42, edited 1 time in total.
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Re: A certain clock rings two notes at quarter past the hour, four notes  [#permalink]

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New post 28 Oct 2019, 14:10
2
D

for the hours:
1 to 5 - 5+4+3+2+1 = 15
8 gongs at each hour = 8*5 =40
total for the hours = 65

for the quarters = 2+4+6 = 12 in each hour.
These occur for hours 1,2,3 and 4. (Not for 5 since it is till 5 pm).
hence 12*4=48

hence total = 65+48=103
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Re: A certain clock rings two notes at quarter past the hour, four notes   [#permalink] 28 Oct 2019, 14:10
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