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705-805 Level|   Math Related|         
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 02:48
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­x, y and z = digits

Min possible x = 2  (If take 1 => y=z)
Max possible x = 2 (If take 3 => 3*4 = 12, z no longer digit and y > x)

2, 2 for both­
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 02:52
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Bunuel
­A student was given an equation, x * y = z,  where x, y, and z are different digits and y > x. Select for Minimum x the least possible value of x, and select for Maximum x the maximum possible value of x. Make only two selections, one in each column.

­
 


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­Digits: \(0 1 2 3 4 5 6 7 8 9\)

\(x * y = z\)
\(x, y, z\) are different digits.
\(y > x\)

\(x\) can not be \(0\) or \(1\) otherwise \(x = z\) or \(y = z\) will happen respectively

So, minumum value for \(x = 2\)

As, \(z\) is also a digit \(=>\) \(z <= 9\)

If we increase \(x\) from then 2 then \(y >= 4 => z >= 12\) which is not possible 

So, maximum value for \(x = 2\)
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 03:10
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According to condition

x*y= z where y>x and x , y, z all are different digits

Thus 2*3=6 can give the minimum value of x=2
Also other possibility 2*4=8 also give the value of x=2 ..there is no possible larger value of x
Thus maximum value of x=2

Thus minimum X= 2 and maximum X = 2
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 03:41
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The least possible value of x will be 1 and greatest value of x will be 6­
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 04:13
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­A student was given an equation, x * y = z, where x, y, and z are different digits and y > x. Select for Minimum x the least possible value of x, and select for Maximum x the maximum possible value of x. Make only two selections, one in each column.


Let' say x=1=> y and z will be same. So x=1 isn't possible
x=2, since y>x=> y=3 or 4
x=3, y min=4 [in this case outcome of Z won't be a digit so not possible]

x=2 is the only solution.
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 04:25
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Ans : Min x = 1 ; Max x = 2

Digits are 0 to 9

x*y = z
where y>x

All are different digits hence 0 is not possible
Also Min value of x is 1 and 1* any thing greater than 1 will give answer in digit


Max value = 2
as 2*3/4 =6/8 satisfies

But 3*4 become 12 which is number not digit

Hence max value of x is 2
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 05:05
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A student was given an equation, x * y = z, where x, y, and z are different digits and y > x. Select for Minimum x the least possible value of x, and select for Maximum x the maximum possible value of x. Make only two selections, one in each column.­

Answer ->

Given -> 
  1. x * y = z
  2. x, y, and z are different digits
  3. y > x
x, y and z lie between 0 and 9 included.

For maximum - 
If z = 9, then factors of 9 are 1, 3, 9. It does not meet the above requirements.

If z = 8, then factors are 1, 2, 4, 8.
8 = 2 * 4, meets the requirements. 2 can be the maximum value that meets the requirements.
Even if we check for z = 7 or z = 6, x = 2 can be the maximum value that meets the requirements.


For mininum - 
If z = 0, it does not meet the above requirements.
Similarly z = 1, 2, 3, 4, 5 does not meet the above requirements.

If z = 6, then factors are 1, 2, 3, 6.
6 = 2 * 3, meets the requirements. 2 can be the minimun value that meets the requirements.

So, x = 2 is the only value.
 
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 05:18
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Bunuel
­A student was given an equation, x * y = z,  where x, y, and z are different digits and y > x. Select for Minimum x the least possible value of x, and select for Maximum x the maximum possible value of x. Make only two selections, one in each column.

­
 


This question was provided by GMAT Club
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­x×y=z
  1. x,y, and z are different digits (0 through 9).
  2. y>x.
  3. z=x×y must be a single digit (0 through 9).

For Minimum x, let's take the options:
  • x=0 and y=1 so z=0 (violate 3rd constraint)
  • x=1 and y=2 so z=2 (violate 3rd constraint)
  • x=2 and y=2 so z=6 (Valid)

Minimum x is 2.

For Maximum x, z should be the maximum which is 9. 9 can be possible with 3x3=9 and 1x9=9 which violates the 2nd and 1st constraints respectively. The next maximum value for z is 8. We have 2 options 2x4=8 and 1x8=8. The second option violates 1st constraint so we choose 1st option: 2x4=8.

Here the maximum x is 2
 ­
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 05:29
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­The answer should be BF
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 05:45
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Minimum x : 1
Maximum x: 2

Given:

(x) * (y) = z

where x, y and z are digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
y > x­

Maximum value of z = 9

Minimum value of x = Maximize value of y
Maximum value of y = Maximize z

Maximum value of z = 9
Maximum value of y = 9

Hence, minimum value of x = 1

Since, x and y are different, minimum value of y is 2.

Maximum value of x = Minimize value of y and Maximize value of z

y >= 2 and x < y
And maximum value of x = 2, since if x = 3, then minimum value of y is 4 but z becomes 12 > 10. Hence cannot be the case
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 05:49
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Minimum value of x cannot be 1.
If x=1 than y=z.(x, y, and z are different digits).

For x=2, y=3 (y > x), z=6
Minimum value of x =2

For x=3, y=4(y > x), z=12 not possible.

Maximum value = Minimum Value =2

Imo 1-2, 2-2
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 06:42
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x*y=z
if x>y
so z>x
z>x>y
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 06:44
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Bunuel
­A student was given an equation, x * y = z,  where x, y, and z are different digits and y > x. Select for Minimum x the least possible value of x, and select for Maximum x the maximum possible value of x. Make only two selections, one in each column.

­
 


This question was provided by GMAT Club
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Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

­
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Based on the given data ­x * y = z,  where x, y, and z are different digits and y > x

x, y and z are different digits 

So x cannot be 0 or 1 Bcs x will be equal to z and y will be equal to z. 

Let x be 2, y=3 then z=6; 
If x=3, y=4 Not possible. 
So the only possible value of x is 2

Hence both max and min value of x is 2. 
 
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 06:48
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Digits are from 0 to 9

xy=z
x,y,z are distinct
we cannot have a case where x=1, y=9 and z=9 . In this case, repition will be there.
So, minimum value of x can't be 1

X can be 2
y can have 4
z will be 8

This is the case where max value of x remains 2.

Overall, x will take only value as 2.
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 07:51
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­A student was given an equation, x * y = z,  where x, y, and z are different digits and y > x. Select for Minimum x the least possible value of x, and select for Maximum x the maximum possible value of x. Make only two selections, one in each column.

­This question need to specifically state that the answer when x and y are multiplied is a single digit number. 
I found it ambigous when you state "digit" to mean single digit. 
 Wouldn't for example your question be refering to numerous digit number by reference "different digits"?
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 08:36
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­A student was given an equation, x * y = z,  where x, y, and z are different digits and y > x. Select for Minimum x the least possible value of x, and select for Maximum x the maximum possible value of x. Make only two selections, one in each column.


possibilities:

x*y=z
2*3=6

other than this won't satisfy the condition

so , 2 is max and min
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GMAT Club Olympics 2024 (Day 9): ­A student was given an equation 19 Jul 2024, 09:55
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1. Clinching facts: (i) x,y,z are all 'different', (ii) they are all 'digits', and (iii) y>x.
2. As per question, multiplication of 2 different digits (x and y) is yielding another digit z (i.e., single numerical figure).
3. Above conditions are met in only 2 cases: (i) 2*3=6 and (ii) 2*4=8. So, in both cases, x can only have the value of 2. Hence, Ans.
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