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CAT Previous Year Paper | CAT Quants Questions | Question 6

One of the most crucial elements of your online CAT preparation is practicing questions from CAT previous year paper to set yourself up for the tricky questions the CAT Question Paper throws at you. You can find yourself stuck in trickier topics like Progressions and hence practicing CAT previous year paper for these topics becomes even more important. Here is a question on progressions from CAT 2020 question paper. Try your hands at this questions and see if you can easily steer through.
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Question 6 : Let the m-th and n-thterms of a Geometric progression be \\frac{3}{4}) and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

  1. -4
  2. -2
  3. 6
  4. 2

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Explanatory Answer

\\frac{3}{4})    12
mth    nth
m > n
Given r is an integer, So rk = \\frac{12}{\frac{3}{4}}) = 16
rk = 24 or 42
Since asked for minimum possible value, Taking rk = {(-2)}2 or {(-4)}2
k = n – m (From m how many terms we have to jump to reach n)
We have two cases r = - 2 and n - m = 4 ----> r + n – m = 2
r = - 4 and n – m = 2 ----> r + n – m = - 2
-2 is the smallest possible value


The answer is, "-2"

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