When you say that the equation n^2 -n is greater than 0 so n could be positive or negative, could you explain that in detail ?
I imagine that the reason is that n is bigger than the square root of n, and the square root of n could be a negative number or a posiitive number...
Many tks. in advance
Hi paki I will try to explain when it is written that n^2 -n>0 it means n*(n-1) > 0 that is both n and n-1 have to be greate than 0 or both have to be smaller than 0 that is that both have to be -ve otherwise
so if n and n-1 are greater than 0 then n minimum value can be 2 as it is integer and if both are -ve then n value can be -2 Hope this clears your doubt
In the formula w=p/trootv, integers p and t are positive constants. If w =2 when v = 1 and if when v = 64, then t = (A) 1 (B) 2 (C) 3 (D) 4 (E) 16
can anyone explain this question coz m nt getting wat exactly it is asking...i think this is incompelte question :confused:
ya..u dont hv the value of w when v=64...cuz when u hv tht value, u will get two equations wid the two soln sets of {w,v} and u can find out values of p and t...
I approach DS problems which deal with integer variables in the following way: (Considering above example)
n-1>0 becomes n>1. So we need to answer whether n>1?
Now consider 1st statement:
n^2 - n > 0
Here, n could be both positive and negative. E.g. n = -2 and n = 2.
For both the cases n^2 - n > 0. However, in one case n > 1 and in another n hence 1 alone is not sufficient.
Now,check 2nd statement:
n^2 = 9.
Here 'n' has 2 possibilities: n = 3 and n = -3.
Again we cannot determine for sure whether n is > 1 or n is So answers A,B and D are out of the window.
Now using both statements together
n^2 = 9 basically gives values n = 3 or -3.
But, the first statement doesn't really help. Hence, we cannot answer this question using both the statements.
Hence answer is 'E'.
HTH :)
thanks deep.
Although I knew the answer i was little confused about when to choose answer choice C. if for instance in the same problem we had statement 1 giving us values 3,4 as possible values for n, will we choose C as the answer, since statement2 says n can be -3 or +3
Hi paki I will try to explain when it is written that n^2 -n>0 it means n*(n-1) > 0 that is both n and n-1 have to be greate than 0 or both have to be smaller than 0 that is that both have to be -ve otherwise
so if n and n-1 are greater than 0 then n minimum value can be 2 as it is integer and if both are -ve then n value can be -2 Hope this clears your doubt
Sillyfool
hi sf,
just to clarify a small thing in the last part of ur explanation. "and if both are -ve then n value can be -2" actually means neffectively means nis my reasoning correct?
folks as part of the solution to this problem,there is a note that says "note that the absolute value expression x2 - must be greater than or equal to 0." Can someone explain this assumption?
folks as part of the solution to this problem,there is a note that says "note that the absolute value expression x2 4 must be greater than or equal to 0." Can someone explain this assumption?
hi raj...absolute value of any real number is always positive.. i.e -x| = x and |x = x...just the absolute distance of number from origin..
(x^2)-4 implies 2 range of values... i.e -2 and x=2, .....(x^2)-4 is non negative and also |(x^2)-4 is positive..
so statement 1 implies y-2>=0.i.e y>2..not sufficient
statement 2...y=14 OR y=-8...not sufficient
Statement 1 & 2 combined : y=14...sufficient ...Ans C
hope solution is correct..pls correct me if am wrong..
folks as part of the solution to this problem,there is a note that says "note that the absolute value expression x2 - must be greater than or equal to 0." Can someone explain this assumption?
I am not an expert in absolute value, but this is my primary reasoning:
First statement:
We have that 3 [(x+2) (x-2)]= y -2
The absolute value is the distance from a number to cero. So is always positive or 0 if the number is 0. Altough x could equal Eg. -2 or 2, the absolute value of the entire expression between [ ] must be positive or cero, but never negative. We cant know the vaule of y with only one equation. So this statement is not suficient.
Second statement:
Y is equal to 14 or -8. Two values, also insuficient.
Answer C. (statement 1 y is positive) + (statement 2) y= 14.
Is that the correct answer? Let me know if I am wrong. Tks.
The expression X2-4 has to be positive here because we are not solving for X but for Y. As we are not solving for X we have no reason to take the X out of modulus sign but to solve it as an absolute value expression.
Now the reason we are taking Y out of mod sign in the second expression is we are solving for Y. So we need to consider both +- values.
Rest answers are well explained by Bhavin and Paki. I hope this helps. Pls post the OA.
The expression X2-4 has to be positive here because we are not solving for X but for Y. As we are not solving for X we have no reason to take the X out of modulus sign but to solve it as an absolute value expression.
Now the reason we are taking Y out of mod sign in the second expression is we are solving for Y. So we need to consider both +- values.
Rest answers are well explained by Bhavin and Paki. I hope this helps. Pls post the OA.
thanks all for your timely responses. I understand mod better now. And the answer to this question is C
Each statement is sufficient. From 1 alone....p is even means p=2,4,6,....or-2,-4,-6......for these values of p, m>1 so m^3>1 From 2 alonep^31 so m^3>1
Each statement is sufficient. From 1 alone....p is even means p=2,4,6,....or-2,-4,-6......for these values of p, m>1 so m^3>1 From 2 alonep^31 so m^3>1
But correct option given is (3) i.e both the statements are required (taken togehter).
=> They have considered 0 as an even integer and hence rejected statement 1 => stament 2 is rejected because when p = -1, m will be equal to .5 only.
There reasoning is both of them togther will suffice but not alone. I think statement 1 alone is sufficient and they have mistakenly considered 0 as an even integer.
But correct option given is (3) i.e both the statements are required (taken togehter).
=> They have considered 0 as an even integer and hence rejected statement 1 => stament 2 is rejected because when p = -1, m will be equal to .5 only.
There reasoning is both of them togther will suffice but not alone. I think statement 1 alone is sufficient and they have mistakenly considered 0 as an even integer.
yes...correct answer is C..
dont forget, 0 is an even integer, but nither positive nor negative.
St 1: p is even If p=0, m=1 and m^3 not greater than 1. for all other even integers, m>1 and hence m^3 greater than 1.. statement 1 not sufficient..A and D out of window..
St 2: pif p=-1, m=-0.5 and m^3 not greater than 1. for all other negative integers p, m>1 and hence m^3 greater than 1.. statement 2 not sufficient..B out of window..
St 1 & 2 combined : i.e p is negative even integer, hence, m>1 and hence m^3 always greater than 1..
2. Is sq.rt(x-3)^2 = 3-x ? a) x not equal to 3 b) -xmod(x) >0
Please plug in with ur answers and explananations.
Hi KingCat,
1. i would go with (C) - both statements taken together are sufficient a) If m-3z > 0, then there can be three cases 1)m and z can be both positive --> m+z >0; 2)both m and z can be negative provided 3z > m---> m+z 3)and m positive and z negative --> cant say whether m+z > 0 or not ....clearly this not sufficient
b) If 4z-m> 0, similar three cases are possible with exception that z alone can't be negative. ...therefore applying the same logic as above it is not sufficient enough
Now, if we take them together, we can easily eliminate second and third cases. if both are negative, it implies that 3z > |m| and at the same time |m| > 4z which not possible. Therefore, z and m can only be positive (if both statements are taken togehter). Hence z+m will always be > 0
2. i will go wuth (B). equation sq.rt(x-3)^2 = 3-x holds true only for x = ( 3, 2, 1, 0, -1, -2, -3...and so on)
a) it includes the values of x > 3 and x 3..not sufficient b) it says that x let me know if u have some other explaination....
