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12 Nov 2018, 00:19
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
40% (02:19) correct
60%
(02:15)
wrong
based on 161
sessions
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Not Attempted Yet
In the XY-plane, region X consists of all the points (x, y) such that 3x + 4y ≤ 12. Is the point (r, s) in region X?
(1) 4r + 3s = 12
(2) r ≤ 4 and s ≤ 3
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) 4r + 3s = 12
(2) r ≤ 4 and s ≤ 3
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
12 Nov 2018, 03:36
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Bunuel
from given eqn 3x+4y<=12
we can find region of the line which would be :
y=-3/4*x+3
slope is -3/4 and points would be (0,3) and ( 4,0)
from statement 1:
4r + 3s = 12
if r=0 , s=4 , (r,s does not fall in region 3x + 4y ≤ 12)
if =3, s=0 ( r,s falls in region 3x + 4y ≤ 12)
in sufficient
from statement 2:
r ≤ 4 and s ≤ 3 all values will fall under region r ≤ 4 and s ≤ 3
r=4 and s=3, we get 16+9=25 no
and r=1, s=1 , 4+3<12 yes
hence option IMO E is correct.
16 Feb 2019, 04:22
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This problem can be solved easily through graphs.
The question says x/4 + y/3 <= 1. And asks us to find if (r,s) falls within that segment i.e. if (r,s) falls below or on the line x/4 + y/3 = 1.
(1) From this, we can get r/3 + s/4 = 1. Plot the line that passes through (3,0) and (0,4). We see that a portion of the line extends beyond the required region. So, insufficient.
(2) A few values that satisfies r<=4 and s<=3 do not fall within the required region. E.g. (4, 3). Hence insufficient.
(1) + (2), we see that a tiny portion that satisfies both the equation doesnt fall under the required region. The tiny portion is denoted by the region shaded in black.
Hence, Ans: E
The question says x/4 + y/3 <= 1. And asks us to find if (r,s) falls within that segment i.e. if (r,s) falls below or on the line x/4 + y/3 = 1.
(1) From this, we can get r/3 + s/4 = 1. Plot the line that passes through (3,0) and (0,4). We see that a portion of the line extends beyond the required region. So, insufficient.
(2) A few values that satisfies r<=4 and s<=3 do not fall within the required region. E.g. (4, 3). Hence insufficient.
(1) + (2), we see that a tiny portion that satisfies both the equation doesnt fall under the required region. The tiny portion is denoted by the region shaded in black.
Hence, Ans: E
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