if m and n are integers such that - Quantitative Aptitude – Indices and Surds |
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The question below is from previous year CAT question from CAT 2019 exam comes from CAT Indices and Surds – if m and n are integers such that …
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CAT 2019 – Slot 1 - Indices and Surds - Question 1 - if m and n are integers such that
Q. 1: If m and n are integers such that (√2)^19 * 3^4 * 4^2 * 9^m * 8^n = 3^n * 16^m (4√64) then m is?
1. -20
2. -24
3. -16
4. -12
Given, √2^19 3^4 4^2 9^m 8^n=3^n 16^m ∜64
Or 2^(19/2)×3^4×2^4×3^2m×2^3n= 3^n×2^4m×2^(6/4)
2^(19/2+4+3n)×3^(4+2m)=3^n×2^((4m+6/4) )
Comparing both sides,
n = 4+2m
19/2 +4 + 3n = 4m + 6/4
Or (19 + 8)/2 + 3(4+2m) = 4m + 3/2
27/2 + 12 + 6m = 4m + 3/2
6m -4m = 3/2 – 27/2 -12
2m = -24
Thus m = -12
Past Year Question Paper & Solutions
Checkout Other Questions of CAT 2019 Slot 1 Paper:
Verbal Ability : | Q.01- Q.05 | Q.06- Q.10 | Q.11- Q.15 | Q.16- Q.20 | Q.21- Q.24 | Q.25- Q.29 | Q.30 – Q.34 |
Logical Reasoning : | Q.01- Q.04 | Q.05- Q.08 | Q.09- Q.12 | Q.13- Q.16 | Q.17- Q.20 | Q.21- Q.24 | Q.25 – Q.28 | Q.29 – Q.32 |
Quantitative Aptitude: | Q.01- Q.05 | Q.06- Q.10 | Q.11- Q.15 | Q.16- Q.20 | Q.21- Q.25 | Q.26- Q.30 | Q.31 – Q.34 |
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