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A store stocks shirts, trousers and suits in the ratio of 4:5:6. If the store stocks only these 3 items, what is the number of items stocked in the store?
(1) The number of suits is 100 more than the number of shirts stocked in the store
(2) The number of suits is 150 less than the number of shirts and trousers stocked in the store
(1) The number of suits is 100 more than the number of shirts stocked in the store
(2) The number of suits is 150 less than the number of shirts and trousers stocked in the store
26 Feb 2020, 01:42
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Questions on Ratios, especially ones like this, test your knowledge of multiples. That’s because in situations like this, you cannot have fractional number of shirts or trousers or suits. So, observe the context of the problem and figure out whether you need to consider fractional values for the ratio or not.
We know that the store does not stock any other item. That’s invaluable too since we do not have to worry about them now.
From the question data, we know that the number of shirts is a multiple of 4, the number of trousers a multiple of 5 and the number of suits a multiple of 6. We can assume them as 4k, 5k and 6k respectively. We are trying to find the total number of items in the store i.e. 15k. We need to be able to find k in order to calculate 15k.
From statement I alone, the number of suits is 100 more than the number of shirts stocked in the store. This means, 6k = 4k + 100. Can we find out k from this equation? Yes we can.
Statement I alone is sufficient. Answer options B, C and E can be eliminated. Possible answer options are A or D.
From statement II alone, the number of suits is 150 less than the number of shirts and trousers. This means, 6k = 9k – 150. Can we find out k from this equation? Positive again.
Statement II alone is sufficient. Answer option A can be eliminated.
The correct answer option is D.
In a DS question, you need not always find the exact answer. As long as you are certain that the given information will give you a definite answer to the question asked, you can stop at that stage and decide on eliminating the wrong answer options at that stage. Practise this technique in as many DS problems as you can so that you start saving time.
Hope that helps!
We know that the store does not stock any other item. That’s invaluable too since we do not have to worry about them now.
From the question data, we know that the number of shirts is a multiple of 4, the number of trousers a multiple of 5 and the number of suits a multiple of 6. We can assume them as 4k, 5k and 6k respectively. We are trying to find the total number of items in the store i.e. 15k. We need to be able to find k in order to calculate 15k.
From statement I alone, the number of suits is 100 more than the number of shirts stocked in the store. This means, 6k = 4k + 100. Can we find out k from this equation? Yes we can.
Statement I alone is sufficient. Answer options B, C and E can be eliminated. Possible answer options are A or D.
From statement II alone, the number of suits is 150 less than the number of shirts and trousers. This means, 6k = 9k – 150. Can we find out k from this equation? Positive again.
Statement II alone is sufficient. Answer option A can be eliminated.
The correct answer option is D.
In a DS question, you need not always find the exact answer. As long as you are certain that the given information will give you a definite answer to the question asked, you can stop at that stage and decide on eliminating the wrong answer options at that stage. Practise this technique in as many DS problems as you can so that you start saving time.
Hope that helps!
26 Feb 2020, 02:52
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No worries, people. This is painfully simple if you just take a moment to understand the mechanics. Realize that when it comes to ratios, they act like rulers: There is only point at which they can make a certain 'measurement' for lack of a better word.
Here, statement (1) clearly gives you a measurement between two ratios, so it's SUFFICIENT.
Statement (2) clearly gives you a measurement between 1 ratio and two others (combined), so it's sufficient as well.
Some people may try to solve this question to get the exact numbers of shirts, trousers, etc. I didn't do any of that or do any work on paper. It therefore took me less than 30 seconds to solve this. People, try to tackle questions like this conceptually. The GMAT is not simply testing whether you get the right answer. It's testing you on time as well!
Here, statement (1) clearly gives you a measurement between two ratios, so it's SUFFICIENT.
Statement (2) clearly gives you a measurement between 1 ratio and two others (combined), so it's sufficient as well.
Some people may try to solve this question to get the exact numbers of shirts, trousers, etc. I didn't do any of that or do any work on paper. It therefore took me less than 30 seconds to solve this. People, try to tackle questions like this conceptually. The GMAT is not simply testing whether you get the right answer. It's testing you on time as well!
