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17 Jan 2025, 01:30
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Difficulty:
65%
(hard)
Question Stats:
65% (02:26) correct
35%
(02:11)
wrong
based on 124
sessions
History
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A store has 75 marbles, each of which is either blue or red in color and either small or large in size. If the number of large marbles is more than the number of small marbles, how many large marbles are in the store?
(1) Of the large marbles, the ratio of the number of blue marbles to the number of red marbles is 3 : 1.
(2) Of the small marbles, the ratio of the number of red marbles to the number of blue marbles is 5 : 6.
(1) Of the large marbles, the ratio of the number of blue marbles to the number of red marbles is 3 : 1.
(2) Of the small marbles, the ratio of the number of red marbles to the number of blue marbles is 5 : 6.
17 Jan 2025, 02:33
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A store has 75 marbles (either blue or red in color and either small or large in size), number of large marbles is more than the number of small marbles:
(1) Of the large marbles, the ratio of the number of blue marbles to the number of red marbles is 3 : 1.
Let the number of Large marbles be L, then Large Blue = 3/4L and Large Red = 1/4L
As no relation to find out L, insufficient.
(2) Of the small marbles, the ratio of the number of red marbles to the number of blue marbles is 5 : 6.
Let the number of Large marbles be S, then Small Blue = 6/11S and Small Red = 5/11S
As no relation to find out S, insufficient.
(1) & (2) Combined:
Although it is tempting to mark as both combined are insufficient as there is no relation given between L and S marbles,
however let's have a look at Blue Marbles:
Total Blue marbles from above relations comes out to:
Total Blue = Large Blue = 3/4L + Small Blue = 6/11S
Now the total number of Blue marbles cannot be a fraction. Also number of Small Blue Marbles and Large Blue Marbles also can't be fractions.
Additionally we know L + S = 75
Also, L>S.
Now to satisfy the above conditions, we need S to be a multiple of 11 and L to be a multiple of 4, such that L>S,
Start trial and error:
S= 11 Then L= 64 (Suitable pair)
S=22 Then L= 53 (Not suitable)
S=33 Then L=42 (Not suitable)
S= 44 Then L= 31 ( Not suitable): Here onwards L<S, hence we need not check for higher values of S.
Hence The only solution: S= 11, L=64.
IMO Ans C
(1) Of the large marbles, the ratio of the number of blue marbles to the number of red marbles is 3 : 1.
Let the number of Large marbles be L, then Large Blue = 3/4L and Large Red = 1/4L
As no relation to find out L, insufficient.
(2) Of the small marbles, the ratio of the number of red marbles to the number of blue marbles is 5 : 6.
Let the number of Large marbles be S, then Small Blue = 6/11S and Small Red = 5/11S
As no relation to find out S, insufficient.
(1) & (2) Combined:
Although it is tempting to mark as both combined are insufficient as there is no relation given between L and S marbles,
however let's have a look at Blue Marbles:
Total Blue marbles from above relations comes out to:
Total Blue = Large Blue = 3/4L + Small Blue = 6/11S
Now the total number of Blue marbles cannot be a fraction. Also number of Small Blue Marbles and Large Blue Marbles also can't be fractions.
Additionally we know L + S = 75
Also, L>S.
Now to satisfy the above conditions, we need S to be a multiple of 11 and L to be a multiple of 4, such that L>S,
Start trial and error:
S= 11 Then L= 64 (Suitable pair)
S=22 Then L= 53 (Not suitable)
S=33 Then L=42 (Not suitable)
S= 44 Then L= 31 ( Not suitable): Here onwards L<S, hence we need not check for higher values of S.
Hence The only solution: S= 11, L=64.
IMO Ans C
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