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Suppose a, b, c and d are positive numbers (not necessarily integers)

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nick1816
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Suppose a, b, c and d are positive numbers (not necessarily integers) [#permalink] New post   29 May 2020, 06:40
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Suppose a, b, c and d are positive numbers (not necessarily integers) . There are 6 possible products obtained by pairing them (namely ab, ac, ad, bc, bd and cd). The values of 5 products (in random order) are 2, 3, 5, 6, 9. Which of the following integers is closest to the sixth product?

A. 3
B. 4
C. 7
D. 8
E. 11
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B
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chetan2u
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Re: Suppose a, b, c and d are positive numbers (not necessarily integers) [#permalink] New post   29 May 2020, 20:51
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nick1816 wrote:
Suppose a, b, c and d are positive numbers (not necessarily integers) . There are 6 possible products obtained by pairing them (namely ab, ac, ad, bc, bd and cd). The values of 5 products (in random order) are 2, 3, 5, 6, 9. Which of the following integers is closest to the sixth product?

A. 3
B. 4
C. 7
D. 8
E. 11



The first thing that comes to my mind is that I can guess the product of all 4 numbers from the given set of products..

Now 2, 3, 5, 6, 9 are values of ab, ac, ad, bc, bd and cd in no particular order.
ab, ac, ad, bc, bd and cd ...\(ab*cd=ac*bd=ad*bc\)
So we have three pairs giving same product

Therefore, the product of 2 pairs out of these 5 should be same .
Only possibility is\( 2*9=3*6=18\).
So the remaining 5th product should also give 18 when multiplied with the missing product..
x*5=18....x=3.6 ~ 4

B
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Re: Suppose a, b, c and d are positive numbers (not necessarily integers) [#permalink] New post   29 May 2020, 21:16
chetan2u wrote:
nick1816 wrote:
Suppose a, b, c and d are positive numbers (not necessarily integers) . There are 6 possible products obtained by pairing them (namely ab, ac, ad, bc, bd and cd). The values of 5 products (in random order) are 2, 3, 5, 6, 9. Which of the following integers is closest to the sixth product?

A. 3
B. 4
C. 7
D. 8
E. 11



The first thing that comes to my mind is that I can guess the product of all 4 numbers from the given set of products..

Now 2, 3, 5, 6, 9 are values of ab, ac, ad, bc, bd and cd in no particular order.
ab, ac, ad, bc, bd and cd ...\(ab*cd=ac*bd=ad*bc\)
So we have three pairs giving same product

Therefore, the product of 2 pairs out of these 5 should be same .
Only possibility is\( 2*9=3*6=18\).
So the remaining 5th product should also give 18 when multiplied with the missing product..
x*5=18....x=3.6 ~ 4

B


Thanks a lot I was trying really hard to solve this for hours. But it's quiet an easy way.

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Rakesh61
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Re: Suppose a, b, c and d are positive numbers (not necessarily integers) [#permalink] New post   30 May 2020, 08:09
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Can someone let me know will this approach work? I tried to get to answer by assuming that as these are Products 2,3,5,6,9 the Products can be formed as
2*1=2
3*1=3
5*1=5
2*3=6
3*3=9
So the 4 terms are 1,2,3,5 now the only Product i get from these 4 thats in the matches optin is 4 as 3 is already in the list. I didnt follow the multiplication

Thanks in advance.

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Re: Suppose a, b, c and d are positive numbers (not necessarily integers) [#permalink] New post   30 May 2020, 08:54
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Rakesh61 wrote:
Can someone let me know will this approach work? I tried to get to answer by assuming that as these are Products 2,3,5,6,9 the Products can be formed as
2*1=2
3*1=3
5*1=5
2*3=6
3*3=9
So the 4 terms are 1,2,3,5 now the only Product i get from these 4 thats in the matches optin is 4 as 3 is already in the list. I didnt follow the multiplication

Thanks in advance.

Posted from my mobile device



No, it will not work as we are not given these are integers.
As in this case answer is 3.6 and approximate value is 4, but if we had to find actual value, then 4 would not be the answer.

May be if it was given a, b, c and d are positive integers, then the values could be 1,2,3, and 5. But then products would be 2,3,5,6,10,15.
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Re: Suppose a, b, c and d are positive numbers (not necessarily integers) [#permalink] New post   16 Oct 2022, 06:23
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Given: Suppose a, b, c and d are positive numbers (not necessarily integers) . There are 6 possible products obtained by pairing them (namely ab, ac, ad, bc, bd and cd). The values of 5 products (in random order) are 2, 3, 5, 6, 9.

Asked: Which of the following integers is closest to the sixth product?

ab*cd = ad*bc = ac*bd
2*9 = 3*6 = 5*x
x = 18/5 = 3.6

IMO B
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Re: Suppose a, b, c and d are positive numbers (not necessarily integers) [#permalink]
16 Oct 2022, 06:23
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