TESTfunda - CAT Question of the Day 14-Jun-12

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Testfunda
14-Jun-12
CAT Question of the Day
Find the number of real solutions of the equation [x] = 2 × ln x. Here ln is natural logarithm and [x] represents the greatest integer less than or equal to x.
OPTIONS
 
 1)0
 2)1
 3)2
 4)3
Tip of the Day
In a test, even after spending a reasonable amount of time on a question if you find that you are not making any head-way, it makes sense to leave that question and forget about it. While solving the next set of questions, avoid mulling over the lost time and reducing your concentration.
Last year's Question of the day (13-Jun-11)
Consider the numbers 819 and 2420. What characteristic is possessed by the remainders obtained when each of the numbers contained in the following series is divided by 819?

(2420 × 1), (2420 × 2), (2420 × 3), (2420 × 4), ....... (2420 × 817), (2420 × 818).
OPTIONS
 
 1)The remainders consist of only prime numbers and one.
 2)The remainders obtained are all co-prime with 819.
 3)The list of remainders consists of all numbers from 1 to 818.
 4)The remainders consist of only prime numbers.
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