12 Days of Christmas GMAT Competition - Day 5: Myrna, Deon, and Kermit

Let the address be ABCDE . where A,B,C,D, E are the single digits less than 10 and different from each other (1). We have:

(2) C = A + B = D + E
(3) C is a factor of both AB and DE
(4) A < B < C
(5) E < D < C

The question asks for DE, which must be within the set of {0, 3, 4 ,5, 7, 8} (6)

From (1), (5) & (6), we only have the following options for DE: 30, 40, 50, 70, 80, 43, 53, 54
Because C must be different from DE, the above list narrows down to 43, 53, 54
From (3), C is a factor of DE, the above list narrows down to 54.

Answer: 54. 4th digit = 5, 5th digit = 4

Let the initials of friends be M, De, K.
Let the numbers be A,B,C,D,E.

M's observation:
A + B =C = D+E

De's observation:
AB/C, DE/C

K's observation:
A<B<C>D>E

More information: all digits are different.

We want to know the values of D and E.

Let's start with C because C has the most hints and is related to all of them.

C is the greatest of them all and is also the sum of the first two and the last two. Therefore, C cannot be 0,1,2,3,4.
Just to explain, why C cannot be 4, let's put C = 4.

C = A+B = D+E, where A,B,D,E<C

therefore, out of A,B,D,E if we put A and B as 1+3, D and E become 2, 0 which cannot sum up to 4.

Put C = 5

A+B = 2+3 ; D+E = 1+4
But,
AB/C = 23/5 or 32/5 is not divisible.
Even if we jumble the numbers with each other, no combination would be divisible by 5.
Therefore, C is not equal to 5.

Put C = 6
A+B = 1+2 ; D+E = 5+4
Also,
AB/C = 12/6 is divisible.
DE/C = 54/6 is divisible.

Therefore, C = 6
That makes D and E as 5 and 4 since D>E.

FINAL ANSWER - 5,4

Checking the values and taking into account that fifth digit must be less than fourth digit: 87, 85, 75, 84, 74, 83 and 73 aren't the answer because the sum of its digits is a two-digit number. 53 and 43 are not the answer either because they are prime numbers.

The answer is 5 as fourth digit and 4 as fifth digit.
Third digit must be 9 and the first two digits can be 18, 27 or 36.

Answers: fourth digit=5 and fifth digit=4

Hi everyone

Straight forward:

__,__,__,__,__

Answer choices can be (in order to get 1 digit in the middle):
4 -> 3
5 -> 3
5 -> 4

let's test each combination:
3 , 6 , 9 , 5 , 4
1. its ascending and descending - 1 rule is correct
2. 9 is a factor of 36 and 54
3. 3+6=9 and 5+4=9

We have our answer: 4th digit is 5 & 5th digit is 4

Let the 5 digit address be:- abcde

we know that:- all are different digits and a < b < c and c > d > e

Out of the options given, "0" cannot be one of the first two or last two digits, since a + b = c = d + e and all 5 are different digits.

Also, fourth digit > fifth digit, so if d = 3 then "e" can only be "0" according to options which is not possible.

if d = 4 then "e" has to be 3. So c = d + e = 7.

But it is also given that "c" is a factor of "de". But 7 is not a factor of 34, hence d is not equal to 4.

Similarly we can check that d =5 and e = 3 is also not possible.

But when d = 5 and e = 4, then c = 9 and 9 is a factor of 54. So this combination satisfies all the conditions.

Hence, fourth digit = 5 and fifth digit = 4

I would say that the whole number is 36954

This number respect all the conditions
3+6=5+4=9
9>6>3 and 9>5>4
36 = 9x4
54 = 9x6

To find the number using the 3 statements provided, we can get that the number is abcde where a < b < c > d > e & 10a + b & 10d + e are factors of c & a+b=c=d+e
Since all the numbers are unique, & given all the statements; the number can be
36954 or 45963

Since, in the options we don't have 6 - the number can only be 36954

Fourth digit - 5
Fifth digit - 4

Myrna, Deon, and Kermit just moved into a new house together and each has made an observation about the numbers in their new five-digit address. Myrna has observed that the first two digits sum to the third digit and that the last two digits also sum to the third digit. Deon has observed that the third digit is a factor of both the two-digit number formed by the first two digits and the two-digit number formed by the last two digits. Kermit has observed that the values of the digits increase from the first to the third digit and then decrease from the third to the fifth digit.

If all of the digits in the address are unique, select from the available options a fourth digit and a fifth digit for the address that are jointly consistent with the information given. Make only two selections, one in each column.

45954 is the five digit address which conforms all the stated regulations.

So, the forth digit is 5 and the fifth digit is 4.

Let A be first digit
Let B be second digit
Let C be third digit
Let D be fourth digit
Let E be fifth digit

A+B = C
D+E = C
10A+B divisible by C
10D+E divisible by C
A<B<C>D>E


As C is the largest and C>D>E; Through try and error, we start from 9
9 = 8+1, 7+2, 6+3, 5+4
Given the answer have 5 and 4, we try whether If D = 5, E = 4 could resolve the answer.

10*5+4 = 54 which is divisible by 9.

Therefore D = 5, E = 4

_ _ _ _ _ -> 5 Digit address
1 2 3 4 5

Myrna: [1] + [2] = [3] and [4] + [5] = [3]
Deon: 3rd digit is a factor of [1][2] & [4][5]
Kermit: [1] < [2] < [3] > [4] > [5]

Possible answers are 3 6 9 5 4 and 4 5 9 6 3.
Since we do not have "6" within the options, 4th digit is 5 and 5th digit is 4.

The sum of the third digit must be between 0 and 9. Hence possible combinations of first and second digits are

0 3

0 4

0 5

0 7

0 8

3 4

3 5

4 5

The third digit in that case

0 3 3

0 4 4

0 5 5

0 7 7

0 8 8

3 4 7

3 5 8

4 5 9

Among all the options,

4 5 9 satisfy the criteria mentioned.

Hence, the number is

4 5 9 5 4

Fourth digit = 5

Fifth digit = 4

To check the necessary conditions, let's look at the given numbers. The last number must be at least third biggest, so 8 is out.

• If it's 7, then: _ _ 9 8 7. However, 87 is not divisible by 9, so it's impossible.
• Let's try 5: _ _ 5. In this case, all four non-center numbers can only be 5-6-7-8, leading to 9 in the middle. But only 45 is divisible by 9, and the number before 5 has to be higher, so it's impossible.
• Let's try 4: 3 6 9 5 4. This works well, so both these numbers (5 and 4) should be the answer.

The answer is: 5(fourth) and 4(last)

In this main hint is
d1<d2<d3>d4>d5

which means 0 can never be a possibility nor same digits in d4 and d5
We have the options left
3, 4, 5, 7, 8

We also know that d3 needs to be single digit sum from the given options, so here again 7 and 8 are eliminated as adding them with any other results in a 2 digit number which wont help us get d3

=>
We have the options left 3, 4, 5

5, 4 ; 5,3 ; 4,3
Now before we check the cases here there is one more point where we know that d3 is a factor of d4d5 and d1d2
So,
4,3 => d3= 4+3 = 7
7 is not a factor 43 (d4d5)
Eliminated

5,3 => d3= 5+3 =8
8 is not a factor of 53 (d4d5)
Eliminated

5,4 => d3 = 4+5 = 9
9 is a factor of 54 (d4d5)
Valid option

d4 = 5
d5 = 4

Nice question