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10 Sep 2018, 20:22
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I have seen that it could be a valuable skill on some tough DS questions esp involving inequality/absolute value etc. However, number picking doesnt come naturally to me. For instance in problems such as
If u(u+v) different from 0 and u >0, is 1/(u+v) < 1/u + v?
1) u+v >0
2) v>0
for st1 since the algebraic approach isnt very easy, when I try to use number plugging-
I have to hold the following three statements in mind:
u(u+v)# 0
u >0
u+v > 0
And then think of numbers that will give two different answers to 1/(u+v) < 1/u + v?
This entire process flips me out. So picking numbers, while relatively easy to put in practice, is uncomfortable, error prone and time consuming method for me.
Where as algebra is far more natural. For instance in St2- algebra is quite straightforward. But algebra is not always obvious and could be really time consuming especially on options where the statement is insufficient. That is probably also why it takes me a lot of time to solve DS problems where answer is E.
Any suggestions to improve number picking skills? Any drills would you guys suggest? Im not looking for advice such as pick all numbers +ve and -ve intigers , +ve and -ve fractions , roots , and zero etc etc. I am looking for how to practically improve this skill
Thanks
If u(u+v) different from 0 and u >0, is 1/(u+v) < 1/u + v?
1) u+v >0
2) v>0
for st1 since the algebraic approach isnt very easy, when I try to use number plugging-
I have to hold the following three statements in mind:
u(u+v)# 0
u >0
u+v > 0
And then think of numbers that will give two different answers to 1/(u+v) < 1/u + v?
This entire process flips me out. So picking numbers, while relatively easy to put in practice, is uncomfortable, error prone and time consuming method for me.
Where as algebra is far more natural. For instance in St2- algebra is quite straightforward. But algebra is not always obvious and could be really time consuming especially on options where the statement is insufficient. That is probably also why it takes me a lot of time to solve DS problems where answer is E.
Any suggestions to improve number picking skills? Any drills would you guys suggest? Im not looking for advice such as pick all numbers +ve and -ve intigers , +ve and -ve fractions , roots , and zero etc etc. I am looking for how to practically improve this skill
Thanks
11 Sep 2018, 13:11
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Hi vincitygialam,
TESTing VALUES (or Picking Numbers; the Tactic can be referred to by a number of different 'titles') is one of the most useful Tactics for the Quant section (it can be used on far more than just the hard questions - up to 2/3 of the questions that you'll see in the Quant section can be beaten with this one approach). I've used that approach - along with Number Properties (which are essentially math rules that you can prove by TESTing VALUES) to solve the problem you posted.
We're told that U(U+V) is not equal to 0 and U > 0. We're asked if 1/(U+V) is less than the sum of 1/U and V. This is a YES/NO question. While it might look complex, it can be handled rather easily by TESTing VALUES and a bit of Number Property knowledge.
1) (U+V) > 0
IF....
U = 1, V = 1, then 1/(1+1) = 1/2 and 1/1 + 1 = 2... 1/2 IS less than 2 and the answer to the question is YES.
U = 1, V = 0, then 1/(1+0) = 1/1 and 1/1 + 0 = 1... 1 is NOT less than 1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT.
2) V > 0
With the information in Fact 2, we know that BOTH U and V are POSITIVE. This allows us to use a particular Number Property rule to our advantage. Regardless of whether you are using positive fractions or positive integers, when BOTH variables are POSITIVE, 1/(U+V) will ALWAYS be LESS than 1/U.
As either (or both) of the values of U or V INCREASE, the value of 1/(U+V) will DECREASE. Obviously 1/U = 1/U, but when you 'add in' a positive value for V to that first fraction, the value of that fraction will DECREASE. Try any positive values for U and V and you'll see. Thus, 1/(U+V) will be LESS than 1/U. Adding V to 1/U simply increases the difference. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.
Final Answer:
To properly master any Tactic (whether Quant or Verbal), you have to practice it repeatedly (first, with the easier prompts - then on tougher and tougher prompts so that you can hone that particular skill). Since you were likely never taught that Tactic in School, it might feel a little 'weird' at first. However, side-by-side, it's almost faster and easier than the traditional 'math' approaches that you might use. The Quant section of the GMAT is NOT a 'math test' - it's a 'critical thinking test' that requires lots of little calculations as you work through it. To maximize your performance in this section, you need to become more of a 'strategist' and less of a 'mathematician.'
GMAT assassins aren't born, they're made,
Rich
TESTing VALUES (or Picking Numbers; the Tactic can be referred to by a number of different 'titles') is one of the most useful Tactics for the Quant section (it can be used on far more than just the hard questions - up to 2/3 of the questions that you'll see in the Quant section can be beaten with this one approach). I've used that approach - along with Number Properties (which are essentially math rules that you can prove by TESTing VALUES) to solve the problem you posted.
We're told that U(U+V) is not equal to 0 and U > 0. We're asked if 1/(U+V) is less than the sum of 1/U and V. This is a YES/NO question. While it might look complex, it can be handled rather easily by TESTing VALUES and a bit of Number Property knowledge.
1) (U+V) > 0
IF....
U = 1, V = 1, then 1/(1+1) = 1/2 and 1/1 + 1 = 2... 1/2 IS less than 2 and the answer to the question is YES.
U = 1, V = 0, then 1/(1+0) = 1/1 and 1/1 + 0 = 1... 1 is NOT less than 1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT.
2) V > 0
With the information in Fact 2, we know that BOTH U and V are POSITIVE. This allows us to use a particular Number Property rule to our advantage. Regardless of whether you are using positive fractions or positive integers, when BOTH variables are POSITIVE, 1/(U+V) will ALWAYS be LESS than 1/U.
As either (or both) of the values of U or V INCREASE, the value of 1/(U+V) will DECREASE. Obviously 1/U = 1/U, but when you 'add in' a positive value for V to that first fraction, the value of that fraction will DECREASE. Try any positive values for U and V and you'll see. Thus, 1/(U+V) will be LESS than 1/U. Adding V to 1/U simply increases the difference. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.
Final Answer:
To properly master any Tactic (whether Quant or Verbal), you have to practice it repeatedly (first, with the easier prompts - then on tougher and tougher prompts so that you can hone that particular skill). Since you were likely never taught that Tactic in School, it might feel a little 'weird' at first. However, side-by-side, it's almost faster and easier than the traditional 'math' approaches that you might use. The Quant section of the GMAT is NOT a 'math test' - it's a 'critical thinking test' that requires lots of little calculations as you work through it. To maximize your performance in this section, you need to become more of a 'strategist' and less of a 'mathematician.'
GMAT assassins aren't born, they're made,
Rich
11 Sep 2018, 17:41
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Bookmarks
Really good question. Whenever you're picking numbers, your goal should to be to "Play Devil's Advocate" - try to find two different answers to the question so that you can prove the statement insufficient. The first set of numbers you pick will always give you one answer which is usually the "obvious" answer, and then from there on out your only goal should be to get a different answer. For example, if you were given something like:
Is the product jkmn = 1?
(1) jk/mn = 1
Your first set of numbers will probably give you "no" (maybe you try j = 8, k = 1, m = 4, n = 2, so that the statement jk/mn = 1 becomes (8 * 1)(4 * 2) = 1 - clearly then the product of 8 * 1 * 4 * 2 is not going to be 1).
From there, your ONLY goal is to try to find numbers that give you the answer "Yes" because you already have a "No" answer. It's a total waste to try really similar numbers (e.g. all positive integers, like 6, 1, 2, and 3) because you'll probably get really similar results. So you want to think "what would it take to get the product equal to 1 so I get a "Yes"?". And that should prompt you to think about fractions:
2 and 1/2, 4 and 1/4
Or about all values being the same:
1, 1, 1, and 1
Either of those would give you your "Yes" and then once you have that you've proven that it's insufficient information and can move on.
Now, that example isn't insanely hard *but* here's what I like about it - it models the thought process of picking numbers in the mindset of "what numbers don't they think I'll think of?" And I really liked that almost immediately when I started practicing DS way back when - some people hate the notion of "shoot they tricked me into not thinking about fractions" but I always liked the idea that the testmaker had challenged me to think of a set of numbers that would go counter to the "obvious." So trying, for example, "hey what if all the variables were the same?" appealed to me - it was that idea of trying to "break" the conventional wisdom.
So you asked how to improve the skill (not just get a list of types of numbers), and I'd suggest two things:
1) Imagine the testmaker sitting across the table from you and think of number picking like a game (chess, poker, any kind of strategy game) where you're matching wits. What numbers does he not want you to think about?
2) Train yourself to look for clues as to what numbers to pick. When you see > 0 or < 0, that means try positive/negative/zero. When you see inequalities, try using the biggest or smallest number they'll let you pick. Again think of it as a game - here they said that u(u+v) is not equal to zero, so which variable should you immediately say "hey they didn't say that THIS couldn't be zero?"- you have to try v = 0 because they left that door open to you. Whenever they specify something about some but not all variables, try that thing for the other variables.
Ultimately if you're that comfortable with algebra you'll probably do a lot of algebra on test day. But in practice, see if you can - even after you've done the algebra to get the answer if you go that way - train yourself to "beat" the testmaker at his/her own game of hiding the number(s) that give "the other" answer.
Is the product jkmn = 1?
(1) jk/mn = 1
Your first set of numbers will probably give you "no" (maybe you try j = 8, k = 1, m = 4, n = 2, so that the statement jk/mn = 1 becomes (8 * 1)(4 * 2) = 1 - clearly then the product of 8 * 1 * 4 * 2 is not going to be 1).
From there, your ONLY goal is to try to find numbers that give you the answer "Yes" because you already have a "No" answer. It's a total waste to try really similar numbers (e.g. all positive integers, like 6, 1, 2, and 3) because you'll probably get really similar results. So you want to think "what would it take to get the product equal to 1 so I get a "Yes"?". And that should prompt you to think about fractions:
2 and 1/2, 4 and 1/4
Or about all values being the same:
1, 1, 1, and 1
Either of those would give you your "Yes" and then once you have that you've proven that it's insufficient information and can move on.
Now, that example isn't insanely hard *but* here's what I like about it - it models the thought process of picking numbers in the mindset of "what numbers don't they think I'll think of?" And I really liked that almost immediately when I started practicing DS way back when - some people hate the notion of "shoot they tricked me into not thinking about fractions" but I always liked the idea that the testmaker had challenged me to think of a set of numbers that would go counter to the "obvious." So trying, for example, "hey what if all the variables were the same?" appealed to me - it was that idea of trying to "break" the conventional wisdom.
So you asked how to improve the skill (not just get a list of types of numbers), and I'd suggest two things:
1) Imagine the testmaker sitting across the table from you and think of number picking like a game (chess, poker, any kind of strategy game) where you're matching wits. What numbers does he not want you to think about?
2) Train yourself to look for clues as to what numbers to pick. When you see > 0 or < 0, that means try positive/negative/zero. When you see inequalities, try using the biggest or smallest number they'll let you pick. Again think of it as a game - here they said that u(u+v) is not equal to zero, so which variable should you immediately say "hey they didn't say that THIS couldn't be zero?"- you have to try v = 0 because they left that door open to you. Whenever they specify something about some but not all variables, try that thing for the other variables.
Ultimately if you're that comfortable with algebra you'll probably do a lot of algebra on test day. But in practice, see if you can - even after you've done the algebra to get the answer if you go that way - train yourself to "beat" the testmaker at his/her own game of hiding the number(s) that give "the other" answer.
