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# If 1/3 of the total number of marbles in the three bags listed in the

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If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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17 Jun 2016, 05:19
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Difficulty:

75% (hard)

Question Stats:

68% (02:16) correct 32% (02:38) wrong based on 982 sessions

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If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

Attachment:

2016-06-17_1618.png [ 22.59 KiB | Viewed 14438 times ]

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Re: If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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17 Jun 2016, 13:56
11
5
Bag P : 10.8% of 37 = 4
Bag Q : 66.7% of x = 2x/3
Bag R : 50% of 32 = 16.

Given, 4 + 2x/3 + 16 = 1/3 ( 37+x+32) => x = 9. Hence B.
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Re: If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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20 Aug 2016, 09:37
FacelessMan wrote:
Bag P : 10.8% of 37 = 4
Bag Q : 66.7% of x = 2x/3
Bag R : 50% of 32 = 16.

Given, 4 + 2x/3 + 16 = 1/3 ( 37+x+32) => x = 9. Hence B.

I have approximated 10.8% as 1/9, which is 11.1%
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If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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21 Aug 2016, 00:17
5
This might look like it contains hard calculations, but the thing to notice here is that the number of balls are always going to be integers.

So, 10.8% of 37 will be 4, we know 50% of x is 32 and we can keep 66.7% as 2/3rds. Once you do this, the question can be solved to arrive at ~9 quickly.
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Re: If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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21 Aug 2016, 05:38
1
3
If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

Total has to be multiple of 3 since 1/3rd of them are blue and 1st and 3rd bag have total 69 marbles so (69 + x)/3 is blue total hence x also must be divisible by 3

hence narrow down to B) 9 or C) 12

66.67 % is nothing but 2/3 rd (ie 33.33 * 2 ie 1/3 * 2)

so if x is 9 then blue marbles in 2nd bag is 6 (2/3rd of 9 = 6)
or if x is 12 then blue marbles in 3rd bag is 8 (2/3rd of 12 = 8)

do that math : if x = 9 then total = 69 + 9 = 78
and total blue = 16 + 4 + 6 = 26
26/78 = 1/3 -----> fits (most likely that B is the ans)

cross check
if x = 12 then total = 81
total blue = 28
28/81 != 1/3 hence (B)
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Re: If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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13 Jun 2017, 04:45
manlog wrote:
I have approximated 10.8% as 1/9, which is 11.1%

10.8% of 37 -> 10% of 37 = 3.7.

3.7 is a little low and the number of balls must be an integer; can round up to 4.
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Re: If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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19 Dec 2017, 07:42
Bunuel wrote:

If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

Attachment:
2016-06-17_1618.png

We are given a table with the following information:

Bag P has 37 marbles and 10.8% of those marbles are blue. So there are 0.108(37) = 3.996, or 4, blue marbles in bag P.

Bag Q has X marble and 66.7% of those marbles are blue. Recall that the fraction 2/3 is approximately 66.7%, so there are (2/3)X blue marbles in bag Q.

Bag R has 32 marbles and 50% of those marbles are blue. So, there are 0.5(32) = 16 blue marbles in bag R.

We are also given that 1/3 of the total marbles in the 3 bags are blue. Thus, we can create the following equation:

1/3(37 + X + 32) = 4 + (2/3)X + 16

Multiplying the equation by 3, we have:

37 + X + 32 = 12 + 2X + 48

X + 69 = 2X + 60

X = 9

There are 9 marbles in bag Q.

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Re: If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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22 Apr 2018, 10:44
Bunuel wrote:

If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

Attachment:
2016-06-17_1618.png

No. of blue marbles in each bag is
Bag P: 10.8% of 37 = 4
Bag Q:66.7% of X = 2/3 X
Bag R: 50% of 32 = 16

Total Blue marbles = 4 + 2/3 X + 16 = 20 + 2/3 X

Also Total marbles count = 37 + X + 32 = 69 + X

So, 1/3 (69+ X ) = 20 + 2/3 X
23 + 1/3 X = 20 + 2/3 X
1/3 X = 3
X = 9

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If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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Updated on: 29 Apr 2018, 03:17
many thanks generis and niks18

yeah working with fractions is easier , also good to know that $$\frac{2}{3}$$= 66%

$$4+16+\frac{2}{3}x= \frac{1}{3} (37+32+x)$$

$$20+\frac{2}{3}x = \frac{1}{3}x+23$$

$$\frac{2}{3}x-\frac{1}{3}x = 3$$

$$\frac{1}{3}x =3$$

$$x =9$$

have a great weekend
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Originally posted by dave13 on 28 Apr 2018, 06:41.
Last edited by dave13 on 29 Apr 2018, 03:17, edited 1 time in total.
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Re: If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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28 Apr 2018, 07:20
dave13 wrote:
Bunuel wrote:

If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

Attachment:
2016-06-17_1618.png

generis, niks18, pushpitkc, hello

here is my unique solution two solutions one is incorrect and next one seems more accurate unfortunately i cant solve 700 level q under 2 min, takes me more time befire i figure out how the problem can be approached

$$4+16+0.67x= \frac{1}{3} (37+32+x)$$

$$20+0.67x =\frac{1}{3}x+23$$

$$20-23 = \frac{1}{3}x-\frac{67}{100}$$

$$-3 = \frac{33}{300}x$$

$$-3 = \frac{11}{100}x$$

the above solution is incorrect, i kept 1/3 as fraction, so i wonder what did i do wrong

in the next solution I converted 1/3 to decimal = 0.33%

$$4+16+0.67x=0.33 (37+32+x)$$

$$20+0.67x = 0.33x+23$$

$$0.67x - 0.33x = 23-20$$

$$3 = 0.34x$$

$$x = 8.8$$

round to the tenth $$8.8$$ and get $$9$$

have a great weekend

hi dave13

Pls check the calculations in the highlighted part above. How come 37+32 become 23? and when you are opening the bracket then each element of the bracket has to be multiplied by 1/3 or 0.33
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If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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28 Apr 2018, 07:30
niks18 wrote:
dave13 wrote:
Bunuel wrote:

If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

Attachment:
2016-06-17_1618.png

generis, niks18, pushpitkc, hello

here is my unique solution two solutions one is incorrect and next one seems more accurate unfortunately i cant solve 700 level q under 2 min, takes me more time befire i figure out how the problem can be approached

$$4+16+0.67x= \frac{1}{3} (37+32+x)$$

$$20+0.67x =\frac{1}{3}x+23$$

$$20-23 = \frac{1}{3}x-\frac{67}{100}$$

$$-3 = \frac{33}{300}x$$

$$-3 = \frac{11}{100}x$$

the above solution is incorrect, i kept 1/3 as fraction, so i wonder what did i do wrong

in the next solution I converted 1/3 to decimal = 0.33%

$$4+16+0.67x=0.33 (37+32+x)$$

$$20+0.67x = 0.33x+23$$

$$0.67x - 0.33x = 23-20$$

$$3 = 0.34x$$

$$x = 8.8$$

round to the tenth $$8.8$$ and get $$9$$

have a great weekend

hi dave13

Pls check the calculations in the highlighted part above. How come 37+32 become 23? and when you are opening the bracket then each element of the bracket has to be multiplied by 1/3 or 0.33

niks18, hello there

to answer your question - How come 37+32 become 23?

$$37+32 =69$$ so$$\frac{1}{3}*69 =23$$ so I get $$23+0,33x$$

$$20+0.67x = 0.33x+23$$

isnt it correct ?
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If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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28 Apr 2018, 07:34
1
dave13 wrote:
Bunuel wrote:

If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

Attachment:
2016-06-17_1618.png

generis, niks18, pushpitkc, hello

here is my unique solution two solutions one is incorrect and next one seems more accurate unfortunately i cant solve 700 level q under 2 min, takes me more time befire i figure out how the problem can be approached

$$4+16+0.67x= \frac{1}{3} (37+32+x)$$

$$20+0.67x = \frac{1}{3}x+23$$

$$20-23 = \frac{1}{3}x-\frac{67}{100}$$

$$-3 = \frac{33}{300}x$$

$$-3 = \frac{11}{100}x$$

the above solution is incorrect, i kept 1/3 as fraction, so i wonder what did i do wrong

dave13
The equation is correct. The arithmetic is off.

(EDIT As niks18 points out), check your math here:
Quote:
$$20-23 = \frac{1}{3}x-\frac{67}{100}$$

$$-3 = \frac{33}{300}x$$

Try using $$\frac{67}{100}=\frac{2}{3}$$

$$\frac{1}{3}x - \frac{2}{3}x$$ = ????

Calculate again and see what you get.

Tip: use fractions with fractions and decimals with decimals. IMO fractions are easier.

Another way to think about setup and solving of the equation . . . (I do not know whether either suggestion will be easier for you - they're just possibilities)

After you replace $$.67$$ with $$\frac{2}{3}$$

Change the setup and cross multiply.

(1) Setup: If blue marbles equal $$\frac{1}{3}$$ of three bags' total marbles:
$$\frac{Blue}{Total}=\frac{1}{3}$$
$$\frac{16+4+\frac{2}{3}x}{37+32+x}=\frac{1}{3}$$

(2) Solve. Cross multiply.

Just one arithmetic mistake, in other words.

Your second solution is correct. If you use decimals (IMO, harder here!) what you calculated is correct.

Hope that helps.
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Re: If 1/3 of the total number of marbles in the three bags listed in the  [#permalink]

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28 Apr 2018, 07:37
1
dave13 wrote:
niks18 wrote:
dave13 wrote:
generis, niks18, pushpitkc, hello

here is my unique solution two solutions one is incorrect and next one seems more accurate unfortunately i cant solve 700 level q under 2 min, takes me more time befire i figure out how the problem can be approached

$$4+16+0.67x= \frac{1}{3} (37+32+x)$$

$$20+0.67x =\frac{1}{3}x+23$$

$$20-23 = \frac{1}{3}x-\frac{67}{100}$$

$$-3 = \frac{33}{300}x$$

$$-3 = \frac{11}{100}x$$

the above solution is incorrect, i kept 1/3 as fraction, so i wonder what did i do wrong

in the next solution I converted 1/3 to decimal = 0.33%

$$4+16+0.67x=0.33 (37+32+x)$$

$$20+0.67x = 0.33x+23$$

$$0.67x - 0.33x = 23-20$$

$$3 = 0.34x$$

$$x = 8.8$$

round to the tenth $$8.8$$ and get $$9$$

have a great weekend

hi dave13

Pls check the calculations in the highlighted part above. How come 37+32 become 23? and when you are opening the bracket then each element of the bracket has to be multiplied by 1/3 or 0.33

niks18, hello there

to answer your question - How come 37+32 become 23?

$$37+32 =69$$ so$$\frac{1}{3}*69 =23$$ so I get $$23+0,33x$$

$$20+0.67x = 0.33x+23$$

isnt it correct ?

hi dave13
yes its correct. my mistake I got confused here. So in your method 1 the mistake is in highlighted part above. kindly check your calculation of 1/3x-67x/100. Rest is ok
Re: If 1/3 of the total number of marbles in the three bags listed in the &nbs [#permalink] 28 Apr 2018, 07:37
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# If 1/3 of the total number of marbles in the three bags listed in the

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