ornaments problem

[divya23]

Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her

collection are handmade, and 1/2 of the handmade ornaments are antiques.

If 1/9 of the ornaments in her collection are handmade antiques, how many

ornaments are in her collection?

1.36
2.60
3.108
4.144
5.180

[Anurag@Gurome]

Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her

collection are handmade, and 1/2 of the handmade ornaments are antiques.

If 1/9 of the ornaments in her collection are handmade antiques, how many

ornaments are in her collection?

1.36
2.60
3.108
4.144
5.180

Let there are N ornaments in her collection.
Then handmade ornaments = N/6 + 10
Antiques = (N/6 + 10)/2 = N/9 implies N = 180

The correct answer is 5.

[divya23]

Let there be N ornaments
handmade = n/6 + 10
antiques = 1/2(n/6+10)
handmade antiques = i cud not get dis thing here can u plz xpain
it shd b n/9
then as per formaula it shd b h + a - ha = total
n/6 +10 + 1/2(n/6+10) - n/9 = n
m not geting this as 180
instead as 108 plz help

[Anurag@Gurome]

Let there be N ornaments
handmade = n/6 + 10
antiques = 1/2(n/6+10)
handmade antiques = i cud not get dis thing here can u plz xpain
it shd b n/9
then as per formaula it shd b h + a - ha = total
n/6 +10 + 1/2(n/6+10) - n/9 = n
m not geting this as 180
instead as 108 plz help

It is mentioned that "1/9 of the ornaments in her collection are handmade antiques", which means if there are N ornaments in her collection, then (1/9) of N = N/9 are antiques, also we have found that (N/6 + 10)/2 are antiques.
So we equate these 2 different expressions to get the value of N.
Hence, (N/6 + 10)/2 = N/9
N/12 + 5 = N/9
5 = N/9 - N/12 (LCM of 9 and 12 = 36)
5 = (4N - 3N)/36
5 = N/36
So, N = 5 * 36 = 180

Hope that helps.

[GMATGuruNY]

Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/9 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?

1.36
2.60
3.108
4.144
5.180

We can plug in the answers, which represent the total number of ornaments.

Answer choice C: 108 ornaments
Handmade = (1/6)*108 + 10 = 28.
Handmade antiques = (1/2)*28 = 14.
Handmade antiques must be (1/9)*108 = 12.
Doesn't work: 14 ≠ 12.
Since (1/9)*108 = 12 is too small, more ornaments are needed.
Eliminate A,B,and C.

Answer choice D: 144 ornaments
Handmade = (1/6)*144 + 10 = 34.
Handmade antiques = (1/2)*34 = 17.
Handmade antiques must be (1/9)*144 = 16.
Doesn't work: 17 ≠ 16.
Eliminate D.

The correct answer is E.

[divya23]

Thank you both of you

[nafiul9090]

Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/9 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?

1.36
2.60
3.108
4.144
5.180

We can plug in the answers, which represent the total number of ornaments.

Answer choice C: 108 ornaments
Handmade = (1/6)*108 + 10 = 28.
Handmade antiques = (1/2)*28 = 14.
Handmade antiques must be (1/9)*108 = 12.
Doesn't work: 14 ≠ 12.
Since (1/9)*108 = 12 is too small, more ornaments are needed.
Eliminate A,B,and C.

Answer choice D: 144 ornaments
Handmade = (1/6)*144 + 10 = 34.
Handmade antiques = (1/2)*34 = 17.
Handmade antiques must be (1/9)*144 = 16.
Doesn't work: 17 ≠ 16.
Eliminate D.

The correct answer is E.

hello mitch

i did the same thing as u. but started from the 1st number. as a result it took me a bit more time. is it always time saving to start from the OP C for this type of problem??

regards nafi

thanks in advance

[vishubn]

Bad wording !! such a easy problem for instance

first it is handmade , and then it says handmade ornaments of antique and then handmade antiques, effectively there are three types of ornaments!!