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

Question

Competition Mode Question

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

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

Verytas · Answer

( 20 x 4 ) + ( 1 + 2 + 3 + 4 + 5 ) = 95.

B

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Peddi · Answer

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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unraveled · Answer

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 [ 37.6 KiB | Viewed 7047 times ]

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

Answer D.

madgmat2019 · Answer

OA:D

joohwangie · Answer

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

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

Archit3110 · Answer

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?

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

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

lacktutor · Answer

—> 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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exc4libur · Answer

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)

Mohammadmo · Answer

4×2 + 4×4 + 4×6 + 9+10+11+12+13= 103

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eakabuah · Answer

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.

saumya2805 · Answer

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

bumpbot · Answer

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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

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