The numbers x and y are not integers. The value of x is closest to which integer?
1. 4 is the integer that is closest to x+y
2. 1 is the integer that is closest to x-y
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value of x is closest to which integer?
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bluementor
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Statement 1: 4 is the integer that is closest to x+yVemuri wrote:The numbers x and y are not integers. The value of x is closest to which integer?
1. 4 is the integer that is closest to x+y
2. 1 is the integer that is closest to x-y
this essentially means (x+y) can be anywhere between 3.5 and 4.5. We can represent this as an inequality:
3.5 < x + y < 4.5
we have no info on y, so insufficient.
Statement 2: 1 is the integer that is closest to x-y
Again, this can be represented in the form of an inequality:
0.5 < x - y < 1.5
here too we do not know anything about y, hence insufficient.
Both statements together:
3.5 < x + y < 4.5
0.5 < x - y < 1.5
add both inequalities:
3.5 + 0.5 < x + y + x - y < 4.5 + 1.5
4 < 2x < 6
2 < x < 3
x can be anywhere between 2 and 3. If x is 2.1, the nearest integer would be 2 and if x is 2.7, the nearest integer would be 3. Insufficient.
Choose E.
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Vemuri
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Cool explanationbluementor wrote:Statement 1: 4 is the integer that is closest to x+yVemuri wrote:The numbers x and y are not integers. The value of x is closest to which integer?
1. 4 is the integer that is closest to x+y
2. 1 is the integer that is closest to x-y
this essentially means (x+y) can be anywhere between 3.5 and 4.5. We can represent this as an inequality:
3.5 < x + y < 4.5
we have no info on y, so insufficient.
Statement 2: 1 is the integer that is closest to x-y
Again, this can be represented in the form of an inequality:
0.5 < x - y < 1.5
here too we do not know anything about y, hence insufficient.
Both statements together:
3.5 < x + y < 4.5
0.5 < x - y < 1.5
add both inequalities:
3.5 + 0.5 < x + y + x - y < 4.5 + 1.5
4 < 2x < 6
2 < x < 3
x can be anywhere between 2 and 3. If x is 2.1, the nearest integer would be 2 and if x is 2.7, the nearest integer would be 3. Insufficient.
Choose E.
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lunarpower
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it shouldn't take too long for you to conclude that the individual statements are insufficient.
statement 1 means that 3.5 < x + y < 4.5
this of course doesn't tell us anything about the sizes of x and y.
for instance, x and y could be 1.5 and 2.5. or, they could be -999.5 and 1003.5.
insufficient by itself.
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statement 2 means that 0.5 < x - y < 1.5
this likewise tells us nothing about the individual values of x and y.
for instance, x and y could be 2.5 and 1.5. or, they could be 1001.5 and 1000.5.
insufficient by itself.
--
together, you can ADD THE INEQUALITIES, so that 'y' cancels out.
(TAKEAWAY: you can add inequalities whenever the 'alligators' - i.e., the "<" or ">" - face the SAME WAY.)
this gives
3.5 < x + y < 4.5
0.5 < x - y < 1.5
add
4 < 2x < 6
therefore
2 < x < 3
this is still insufficient, because x could be closer to 2, closer to 3, or neither (if it's exactly in the middle, at 2.5).
ans (e).
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you could also just LOOK FOR SPECIFIC NUMBERS that satisfy the criteria in the problem. for instance, x = 2.7 and y = 1.5 satisfy both statements, making x closest to 3. also, x = 2.3 and y = 1.5 satisfy both statements, making x closest to 2.
so, both statements together are still insufficient, so, (e).
statement 1 means that 3.5 < x + y < 4.5
this of course doesn't tell us anything about the sizes of x and y.
for instance, x and y could be 1.5 and 2.5. or, they could be -999.5 and 1003.5.
insufficient by itself.
--
statement 2 means that 0.5 < x - y < 1.5
this likewise tells us nothing about the individual values of x and y.
for instance, x and y could be 2.5 and 1.5. or, they could be 1001.5 and 1000.5.
insufficient by itself.
--
together, you can ADD THE INEQUALITIES, so that 'y' cancels out.
(TAKEAWAY: you can add inequalities whenever the 'alligators' - i.e., the "<" or ">" - face the SAME WAY.)
this gives
3.5 < x + y < 4.5
0.5 < x - y < 1.5
add
4 < 2x < 6
therefore
2 < x < 3
this is still insufficient, because x could be closer to 2, closer to 3, or neither (if it's exactly in the middle, at 2.5).
ans (e).
--
you could also just LOOK FOR SPECIFIC NUMBERS that satisfy the criteria in the problem. for instance, x = 2.7 and y = 1.5 satisfy both statements, making x closest to 3. also, x = 2.3 and y = 1.5 satisfy both statements, making x closest to 2.
so, both statements together are still insufficient, so, (e).
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
