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A pantry holds x cans of beans, twice as many cans of soup, and half a

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Bunuel
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A pantry holds x cans of beans, twice as many cans of soup, and half a [#permalink] New post   23 May 2019, 21:42
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A pantry holds x cans of beans, twice as many cans of soup, and half as many cans of tomato paste as there are cans of beans. If there are no other cans in the pantry, which of the following could be the total number of cans in the pantry?

I. 7
II. 45
III. 63


A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
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D
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Re: A pantry holds x cans of beans, twice as many cans of soup, and half a [#permalink] New post   23 May 2019, 22:28
Bunuel wrote:
A pantry holds x cans of beans, twice as many cans of soup, and half as many cans of tomato paste as there are cans of beans. If there are no other cans in the pantry, which of the following could be the total number of cans in the pantry?

I. 7
II. 45
III. 63


A. I only
B. II only
C. III only
D. I and III only
E. I, II and III


read as follows-
A pantry holds x cans of beans (let x)
twice as many cans of soup, as there are cans of beans (2x)
half as many cans of tomato paste, as there are cans of beans (x/2)
Now total: x + 2x + x/2 = (7x/2), X>0 Integer

I. 7 possible for x=2.
II. 45 not possible for any value of x
III. 63 possible for x=18.

D. I and III only.
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Re: A pantry holds x cans of beans, twice as many cans of soup, and half a [#permalink] New post   24 May 2019, 10:06
Bunuel wrote:
A pantry holds x cans of beans, twice as many cans of soup, and half as many cans of tomato paste as there are cans of beans. If there are no other cans in the pantry, which of the following could be the total number of cans in the pantry?

I. 7
II. 45
III. 63


A. I only
B. II only
C. III only
D. I and III only
E. I, II and III


from given info we can say
x+x/2+x = answer optios
7x/2 = answer options
so test with given options only 1 & 3 are valid integer value s
IMO D
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Re: A pantry holds x cans of beans, twice as many cans of soup, and half a [#permalink] New post   25 Oct 2020, 14:21
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Bunuel wrote:
A pantry holds x cans of beans, twice as many cans of soup, and half as many cans of tomato paste as there are cans of beans. If there are no other cans in the pantry, which of the following could be the total number of cans in the pantry?

I. 7
II. 45
III. 63


A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Solution:

Let t be the number of cans of tomato paste. Since the number of cans of tomato paste is half the number of cans of beans, there are 2t cans of beans in the pantry. Since the number of cans of soup is twice the number of cans of beans, there are 4t cans of soup in the pantry. Thus, the total number of cans in the pantry is t + 2t + 4t = 7t. As we can see, the number of cans in the pantry is a multiple of 7. Thus, the two multiples of 7 among the answer choices (which are 7 and 63) are possible values for the total number of cans.

Answer: D
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Re: A pantry holds x cans of beans, twice as many cans of soup, and half a [#permalink]
25 Oct 2020, 14:21
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