How to address such questions..??.. CG makes me go nuts..:banghead:
===== In the xy-plane, is the slope of line k positive? (1) Line k passes through the points (-1, -7) and (2, 5). (2) Line k has equation y = 4x 3. ===== In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l? (1) The product of the slopes of line l and line k is 1. (2) Line k passes through the origin. =====
for the first ques the ans is D(IMO). From 1) u can calc slope. so A alone is suff. From 2) we can calc the slope from y=mx+C so slope is +ve.
For the 2nd ques
we want the slope of line l.
Take 1)we can only know that the 2 lines are perpendicular.
SO 1) alone is insuff
Take 2) we have no info on line l so insuff.
take 1) and 2) here we have 2 points for k so we can calc slope of K and so we can calc slope for l since k and l are perpendicular.
For the first one,compare the lines with the standard equation of y=mx+c and if m positive slope positive. for first statement- m=(5+7)/(2+1)=4 second statement,m=4 so either is suffeciet-D
2.answer is C. from the point of intersection, the two equations will be- k=>12=16m'+5c' l=>12=16m"+5c"
from first statement m'*m"=-1 and from second statement 5C'=0,m'=3/4 so m"=-4/3.
Hey guywithguts, U need not actually calculate the values to answer this particular question.
Time to try some tough one... IS X a negative number?
1) X^2 is a positive number 2) x. Y| is not a positive number
From 1. X not equal to 0. x can take both +ve and -ve. so cannot ans from 1. From 2: x.y is zero or -ve. a.if y is not 0 , x has to be -ve . => not +ve b.If y=0 then x can take any number. => not +ve c. y any number ( 0 , -ve,+ve) and x is 0. => not +ve so, from 2 we cannot conclude whether x is -ve. from 1 & 2 : x is not equal to 0. cases a, b. nothing says Y is is not zero so 1 and 2 are not sufficient to ans the q
If a & b are integers, and a| > |b|, is a.|b1) a b) ab >= 0.
from 1. a| > |b and a b can be 0,+ve ( but so range of b can be (-a,a)
a.b so 1 is not sufficient.
from 2.
a| > |b implies a|-|b > 0
a cannot be 0. but b can be 0
for ab>=0 If a > 0 , b (0,+ve) if a is a.|bfails when any a,b are +ve
Option 1: X^2 = positive number X can be +ve or -ve. NOT SUFF
Option 2: X.Y|
+ve now, Y is always +ve but
+ve can mean X.Y| = -ve or X.Y = 0 NOT SUFF
Now taking option 1 and option 2 together, we find that X is -ve.. thus correct answer must be option C
hey varun ...not necessary that x wud be -ve. St 2 has 2 alternatives. y could be zero and x could be any real no OR x is -ve ... So combines we cannot sat that x is necessarily negative ...
hey varun ...not necessary that x wud be -ve. St 2 has 2 alternatives. y could be zero and x could be any real no OR x is -ve ... So combines we cannot sat that x is necessarily negative ...
Ans E
Well I was left with only C and E to chose from.. but if u wud combine the 2 option in the question u wud see that both option give X as possibly -ve.. which kinda reinforces that X is not 0 and not +ver either.. thats' how -ve..
Time to try some tough one... IS X a negative number?
1) X^2 is a positive number 2) x. Y is not a positive number
Well I was left with only C and E to chose from.. but if u wud combine the 2 option in the question u wud see that both option give X as possibly -ve.. which kinda reinforces that X is not 0 and not +ver either.. thats' how -ve..
your thoughts..!!..
well..
St 1 : x is +ve or -ve St 2: x. Y is not a positive number implies product is 0 or -ve
possibilities: a) X=0 and Y is any no OR b) x= any real no and y = 0 OR c) x= -ve and y = any no
combined statements :
It tells us x is not zero ...so option a) of St 2 is gone ... But still we cannot rule out option b and c of statement 2 ..
Or in other words, x can be any real no (which includes positive no) Or -ve ..still no concensus whether x is -ve ...
Yesterday Diana spent a total of 240 minutes attending a training class, responding to Emails, and talking on the phone. If she did no two of these three activities at the same time, how much time did she spend talking on the phone? (1) Yesterday the amount of time that Diana spent attending the training class was 90 percent of the amount of time that she spent responding to E-mails. (2) Yesterday the amount of time that Diana spent attending the training class was 60 percent of the total amount of time that she spent responding to E-mails and talking on the phone.
