Quantitative Aptitude - Algebra - Inequalities - For how many integers n
Quantitative Aptitude - Algebra - Inequalities
Question
For how many integers n, will the inequality (n â€“ 5) (n â€“ 10) â€“ 3(n â€“ 2) â‰¤ 0 be satisfied?
Answer
11
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Inequalities, we can see that,
On solving the equation, we get n^2 â€“ 18n + 56 â‰¤ 0
Factorize and we get, (n-4)(n-14) â‰¤ 0
4 â‰¤ n â‰¤ 14
No of values of n =11
Answer: 11
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Quantitative Aptitude - Algebra - Inequalities - The number of solutions (x, y, z)
Quantitative Aptitude - Algebra - Inequalities
Question
The number of solutions (x, y, z) to the equation x â€“ y â€“ z = 25, where x, y, and z are positive integers such that x â‰¤ 40, y â‰¤ 12, and z â‰¤ 12 is
A) 101
B) 99
C) 87
D) 105
Answer
Option (B)
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Inequalities, we can see that,
x = 25 + y + z. The possible values of x, y, z and the corresponding number of values of y, z are

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Quantitative Aptitude â€“ Algebra - Inequalities â€“ If N and x are positive integers
Slot -2 â€“Â Quantitative Aptitude â€“ Algebra - Inequalities â€“ If N and x are positive integers
If N and x are positive integers such that N^N = 2^160 and N^2 + 2^N is an integral multiple of 2^x, then the largest possible x is?
Answer: 10
Solution: N^N = (2^5)^32
N^N = 32^32
N=32
32^2 + 2^32 = (2^5)^2 + 2^32
32^2 + 2^32 = 2^10 + 2^32
32^2 + 2^32 = 2^10(1 + 2^22)
Hence, Largest possible value of x is 10.
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Quantitative Aptitude â€“ Algebra - Inequalities â€“ The smallest integer n such that n^3
Slot -2 â€“Â Quantitative Aptitude â€“ Algebra - Inequalities â€“ The smallest integer n such that n^3
The smallest integer n such that n^3 - 11n^2 + 32n - 28 > 0 is?
Answer: 8
Solution:
Given, n^3 - 11n^2 + 32n - 28 > 0
(n-7) (n-2)^2>0
Therefore n must be greater than 7.
So smallest integral value of n = 8
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