For positive integers a and b, let a triangle b be defined as ab+1. If x and y are positive integers and x triangle y equals 16, which of the following could be a value of y? I.1 II. 2 III. 3 (A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III

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Sandhya Repala

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xy +1=16 then xy=16-1=15 xy=15 then y can be 1 or 3 as 1 and 3 are factors of 15
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Math magician

C
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Math Magician

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I am a Mechanical engineer having 7 years of teaching experience of Maths , Physics and chemistry

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SME in Mathematics & Statistics

x triangle y = 16 xy + 1 = 16 xy = 15 since, x and y are positive integers, y can take values 1, 3 or 5. From the options, y can be 1 or 3. Hence, correct option is (C) I and III only.
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Maths Tutor upto Graduation level

As it is given to you that x triangle y = 16 and x triangle y means xy+1 so, xy + 1 = 16 or xy = 15 since, x and y are positive integers, so the product will be 15 only when x and y are any of the following pairs: (1,15),(3,5),(5,3),(15,1). So, the possibility of y are 1,3,5 and 15. Here the options...
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As it is given to you that x triangle y = 16 and x triangle y means xy+1 so, xy + 1 = 16 or xy = 15 since, x and y are positive integers, so the product will be 15 only when x and y are any of the following pairs: (1,15),(3,5),(5,3),(15,1). So, the possibility of y are 1,3,5 and 15. Here the options are 1and3 as no 5 and 15 are given in the choices. Hence, y can take values 1 and 3. So, go with C. From the options, y can be 1 or 3. Hence, correct option is (C) I and III only. read less
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Lecturer in Mathematics in IIT level, 22 years experience and qualification M.Sc(Maths)

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The equation will be xy+1=16 xy=15 means x and y should be factor of 15 so y can have 1 or 3 C is the correct option
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C
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C: I and III only
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