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Fill in each of the empty spaces between the numbers

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Jihyo
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Fill in each of the empty spaces between the numbers [#permalink] New post   24 Apr 2021, 03:23
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Fill in each of the empty spaces between the numbers in the following series with symbols +,-,/ and * ( use each symbol only once and no parenthesis ).What is the least possible value of the result?
1__3__5__7__9=?

A) -5.29
B)57.67
C)-61.4
D)-2.3
E)-3.29
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C
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AndrewN
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Re: Fill in each of the empty spaces between the numbers [#permalink] New post   24 Apr 2021, 09:06
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Jihyo wrote:
Fill in each of the empty spaces between the numbers in the following series with symbols +,-,/ and * ( use each symbol only once and no parenthesis ).What is the least possible value of the result?
1__3__5__7__9=?

A) -5.29
B)57.67
C)-61.4
D)-2.3
E)-3.29

Good question. If we want to derive the least possible value, we would think that the last two blanks ought to be "-" and "*," respectively, since we would then be subtracting the largest possible value from the first half:

1__3__5 - 7 * 9 = 1__3__5 - 63

With only two blanks to go, the rest is a simple thought exercise:

Option #1 (+, /)

\(1 + \frac{3}{5} = 1 \frac{3}{5}\)

Option #2 (/, +)

\(\frac{1}{3} + 5 = 5 \frac{1}{3}\)

Obviously, we want the first outcome, so the entire sequence should be

\(1 + \frac{3}{5} - 7 * 9 = 1.6 - 63 = - 61.4\)

The answer is (C).

- Andrew
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Re: Fill in each of the empty spaces between the numbers [#permalink] New post   24 Apr 2021, 09:10
Hello AndrewN. How would you find the maximum value?
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Re: Fill in each of the empty spaces between the numbers [#permalink] New post   24 Apr 2021, 09:18
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Jihyo wrote:
Hello AndrewN. How would you find the maximum value?

Hello, Jihyo. I would apply the same logic with the 7 and 9 but add them this time and then look to maximize the first half. So, with "+" and "*" out of the way, we would only need to consider "-" and "/":

\(1 - \frac{3}{5} + 7 * 9 = 0.4 + 63 = 63.4\)

- Andrew
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Re: Fill in each of the empty spaces between the numbers [#permalink] New post   29 Apr 2021, 00:07
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1 + 3 / 5 - 7 * 9 = -61.4


Reasoning:


To get the least possible value we want to have the highest possible magnitude of a negative value we can get.

So i started by multiplying the last 2 numbers (7 * 9)

And then stuck the (-) in front of it:

1......3.....5 - 7 * 9

1........3....5 - 63

Then at this point, we want to have the lowest magnitude possible for the inevitable positive value in front. This way we can keep as much of the -63 as possible.

If we put a division sign in between the 3 and 5 and then added 1, this would only take away 1 and 3/5 from the -63


1 + 3 / 5 - 7 * 9

PEMDAS -division and multiplication first

1 + (3/5) - 63

1.6 - 63

-61.4

(C)

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Re: Fill in each of the empty spaces between the numbers [#permalink] New post   29 Apr 2021, 00:35
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Jihyo wrote:
Fill in each of the empty spaces between the numbers in the following series with symbols +,-,/ and * ( use each symbol only once and no parenthesis ).What is the least possible value of the result?
1__3__5__7__9=?

A) -5.29
B)57.67
C)-61.4
D)-2.3
E)-3.29



You need the minimum value. Note that most options are negative. So what you are looking for is a negative answer which is the least. It means that we need to maximise the absolute value.
Multiplication multiplies the value and hence increases it the most. So to maximise absolute value, let's keep multiplication between 7 and 9. Let's make it negative by putting "-" in front of 7.

The addition should be minimum to decrease its impact on our negative value. So put "+" between 1 and 3 and divide 3 by 5

1 + 3 / 5 - 7 * 9
We get -61.4 which is the lowest option.

Answer (C)
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Re: Fill in each of the empty spaces between the numbers [#permalink] New post   29 Apr 2021, 04:00
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Solution:

Observe the options. Four of them bear a - sign. Question is how do we reach it?

* and + will increase the value. Keep it for the large digits to maximise and use a - sign to maximise the negative number so obtained.

=> - 7 * 9

Now, we need to operate 1,3,5 in a way so that they create a minimum value that on subtracting from the result above creates a large negative number.

Can we do 1/3+5 ? We would have 5.33 to be subtracted from then

Can we do 1+3/5 ? We would certainly get less than 5.33 = 1.6 and must use this to get the largest negative possible here

So all in all, 1+ 3/5 -7 *9 = -61.4 (option c)

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SahilGera18
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Re: Fill in each of the empty spaces between the numbers [#permalink] New post   29 Apr 2021, 12:40
HI

1/3*5+7-9==-0.333

Why this cant be the solution?

Also please explain your method.
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Re: Fill in each of the empty spaces between the numbers [#permalink] New post   29 Apr 2021, 18:26
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Because the answer would not be the least possible value.


-0.333 > -61.4

All the numbers start blurring together after too much practice. I’ve been there too many times lol.

SahilGera18 wrote:
HI

1/3*5+7-9==-0.333

Why this cant be the solution?

Also please explain your method.


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Re: Fill in each of the empty spaces between the numbers [#permalink]
29 Apr 2021, 18:26
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