lunarpower wrote:

swati.arunahuja wrote:Hi,

I'm particularly weak in the DS questions pertaining to Inequalities. Would any have any last minute piece of advise for me?
Also, I'm taking the test dayafter, so your last minute advise is most welcome:)
Thanks in advance

there are only a couple of things you really have to know about inequalities, but the number of ways in which those things are combined is almost endless.

here are the facts you need to know:

* when you have SIMULTANEOUS INEQUALITIES, here's the simplest guideline to follow:
- ADD only
- MAKE SURE THE INEQUALITY SIGNS FACE THE SAME WAY

for instance, if you are given the inequalities z - 3m > 0 and 4m - z > 0, you can add those in their current state (since both of the inequality signs are "greater than") to yield m > 0.

if you are given, say, a < b and c > d, and you wanted to combine them, you'd simply turn one of them around by multiplying by a negative quantity, usually -1:
-a > -b
c > d
add: c - a > d - b
there are rules you could memorize for subtracting inequalities, but they're a pain - you have to make sure the inequality signs are facing opposite ways, and, worse yet, you have to know which way the sign is supposed to face after you perform the subtraction. that is not friendly - and it produces the same result as multiplying one side by -1 and then adding anyway.

* do not ever forget to FLIP THE INEQUALITY SIGN when you MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
also, corollary: if you DON'T KNOW THE SIGN OF A VARIABLE in an inequality, YOU CAN'T DIVIDE OR MULTIPLY BY IT.
this means that you can't "cross multiply" most inequalities, because cross multiplying is really multiplying by both denominators.
see https://www.manhattangmat.com/forums/if- ... t2997.html for a problem of this type, on which i made copious comments about what you can and can't do with inequalities (sorry for the cross posting).

lunarpower wrote:

swati.arunahuja wrote:Hi,

I'm particularly weak in the DS questions pertaining to Inequalities. Would any have any last minute piece of advise for me?
Also, I'm taking the test dayafter, so your last minute advise is most welcome:)
Thanks in advance

there are only a couple of things you really have to know about inequalities, but the number of ways in which those things are combined is almost endless.

here are the facts you need to know:

* when you have SIMULTANEOUS INEQUALITIES, here's the simplest guideline to follow:
- ADD only
- MAKE SURE THE INEQUALITY SIGNS FACE THE SAME WAY

for instance, if you are given the inequalities z - 3m > 0 and 4m - z > 0, you can add those in their current state (since both of the inequality signs are "greater than") to yield m > 0.

if you are given, say, a < b and c > d, and you wanted to combine them, you'd simply turn one of them around by multiplying by a negative quantity, usually -1:
-a > -b
c > d
add: c - a > d - b
there are rules you could memorize for subtracting inequalities, but they're a pain - you have to make sure the inequality signs are facing opposite ways, and, worse yet, you have to know which way the sign is supposed to face after you perform the subtraction. that is not friendly - and it produces the same result as multiplying one side by -1 and then adding anyway.

* do not ever forget to FLIP THE INEQUALITY SIGN when you MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
also, corollary: if you DON'T KNOW THE SIGN OF A VARIABLE in an inequality, YOU CAN'T DIVIDE OR MULTIPLY BY IT.
this means that you can't "cross multiply" most inequalities, because cross multiplying is really multiplying by both denominators.
see https://www.manhattangmat.com/forums/if- ... t2997.html for a problem of this type, on which i made copious comments about what you can and can't do with inequalities (sorry for the cross posting).

lunarpower wrote:

swati.arunahuja wrote:Hi,

I'm particularly weak in the DS questions pertaining to Inequalities. Would any have any last minute piece of advise for me?
Also, I'm taking the test dayafter, so your last minute advise is most welcome:)
Thanks in advance

there are only a couple of things you really have to know about inequalities, but the number of ways in which those things are combined is almost endless.

here are the facts you need to know:

* when you have SIMULTANEOUS INEQUALITIES, here's the simplest guideline to follow:
- ADD only
- MAKE SURE THE INEQUALITY SIGNS FACE THE SAME WAY

for instance, if you are given the inequalities z - 3m > 0 and 4m - z > 0, you can add those in their current state (since both of the inequality signs are "greater than") to yield m > 0.

if you are given, say, a < b and c > d, and you wanted to combine them, you'd simply turn one of them around by multiplying by a negative quantity, usually -1:
-a > -b
c > d
add: c - a > d - b
there are rules you could memorize for subtracting inequalities, but they're a pain - you have to make sure the inequality signs are facing opposite ways, and, worse yet, you have to know which way the sign is supposed to face after you perform the subtraction. that is not friendly - and it produces the same result as multiplying one side by -1 and then adding anyway.

* do not ever forget to FLIP THE INEQUALITY SIGN when you MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
also, corollary: if you DON'T KNOW THE SIGN OF A VARIABLE in an inequality, YOU CAN'T DIVIDE OR MULTIPLY BY IT.
this means that you can't "cross multiply" most inequalities, because cross multiplying is really multiplying by both denominators.
see https://www.manhattangmat.com/forums/if- ... t2997.html for a problem of this type, on which i made copious comments about what you can and can't do with inequalities (sorry for the cross posting).