Hi, there. I'm happy to help with these:
1) What is the total value of negotiated stocks of company X in 97?
Let x = value of stocks in 1997.
Statement #1:
In 98, the value of a stock of company X increased 4% in relation of 97
Let y = value of stocks in 1998. This tells us y = 1.04*x. We have two variables, and don't know the value of either, only the relationship. Statement #1, by itself, is
insufficient.
Statement #1:
The total negotiated stocks of company X in 98 was 1,800,000
Here y = 1,800,000. But, we have no connection with x (remember not to carry information from Statement #1 into Statement #2!) Statement #2, by itself, is
insufficient.
Combined Statements #1 & #2:
From #2, we have y = 1,800,000
From #1, we have y = 1.04*x
Combining, we have 1,800,000 = 1.04*x, and we could solve for x.
Combined, the statements are
sufficient.
Answer to #1 =
C
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2. What is the greatest term of the series with four consecutive even numbers?
Statement #1:
The sum of the last two numbers is 30
The only two consecutive even number that add to 30 are 14 + 16. If these are the last two in the series, then the greatest number is 16. Statement #1, by itself, is
sufficient.
Statement #2:
The sum of the first two numbers is 22
The only two consecutive even number that add to 22 are 10 + 12. If these are the first two in the series, then the series must be 10, 12, 14, 16, and 16 is the highest number in the series. Statement #2, by itself, is
sufficient.
Answer to #2 =
D
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3)
Elements in Set S are represented by an = n/(n+1), (n≥1).All elements are different. Is there a number in S greater than 19/24?
When n gets large, the expression n/(n+1) approaches 1, so it gets bigger than 19/24.
n = 1 ---> a1 = 1/2 = 12/24 < 19/24
n = 2 ---> a2 = 2/3 = 16/24 < 19/24
n = 3 ---> a3 = 3/4 = 18/24 < 19/24
n = 4 ---> a4 = 4/5 = 96/120 > 95/120 = 19/24
n = 5 ---> a5 = 5/6 = 20/24 > 19/24
All subsequent terms will get closer and closer to 1, so will get progressively bigger than 19/24.
So, for terms from n = 1 to n = 3, the an is less than 19/24, and for all terms n≥5, an will be greater than 19/24.
Statement #1:
One number is S is 5/6
Here, they just give us a member of S bigger than 19/24, so we can answer "yes" to the prompt question. Statement #1, by itself, is
sufficient.
Statement #2:
There are 5 numbers in S
As we saw above, all the whole infinity of possible members of S, there are only three possible members that are less than 19/24. Since all five members of S are different, then at least two must be greater than 19/24. Statement #2, by itself, is
sufficient.
Answer to #3 =
D
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https://gmat.magoosh.com/lessons/363-avo ... kes-part-i
At Magoosh, we have 200+ video lessons. We have a sale ending on Thursday, so it's particularly good time to take advantage of Magoosh.
Does all this make sense? Let me know if you have any questions on what I've said.
Mike
