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In the problem below, AB, CD, and EF are two-digit numbers, where A, B

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In the problem below, AB, CD, and EF are two-digit numbers, where A, B [#permalink] New post   Updated on: 21 Nov 2021, 02:35
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In the problem below, AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.

AB + CD = EF

Is F prime?

(1) B and D are consecutive integers.
(2) C = 8.
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C

Originally posted by vishnugmatgupta on 20 Nov 2021, 20:38.
Last edited by Bunuel on 21 Nov 2021, 02:35, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In the problem below, AB, CD, and EF are two-digit numbers, where A, B [#permalink] New post   21 Nov 2021, 02:54
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In the problem below, AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.

AB + CD = EF

Is F prime?

(1) B and D are consecutive integers.
So F could be 1+2 or 2+3 or 3+4. In each case answer is yes.
Or F could be 4+5, in which case answer is no.
Insufficient

(2) C = 8.
Nothing about F.
AB+8D=EF. Only thing we can say that A is 1.
Insufficient

Combined
As A is 1, E is 1+8 or 9.
Since E is 9, F will not be 9.
Only possible cases are 3, 5 or 7, all of which are primes.
Sufficient


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In the problem below, AB, CD, and EF are two-digit numbers, where A, B [#permalink] New post   22 Nov 2021, 12:25
vishnugmatgupta wrote:
In the problem below, AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.

AB + CD = EF

Is F prime?

(1) B and D are consecutive integers.
(2) C = 8.


Statement 1 Alone:

Since B + D = F (or B + D = 10 + F) and B & D have opposite parity, we know F must be odd. F can be 2 + 3 = 5 (prime) or 4 + 5 = 9 (not prime), however, so statement 1 alone is insufficient.

Statement 2 Alone:

Since the result is a two-digit number, we must have A = 1 and E = 9 with this information. However, we don't know F, statement 2 alone is insufficient.

Both Statements Combined:

We have used up 1, 8, and 9. Most importantly, we confirm we cannot have any carrying from the unit digits. Then B + D = F must be 2 + 3 = 5, or 3 + 4 = 7 (we already used up 9 so F cannot be 9). Then combined it is insufficient.

Answer: E
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In the problem below, AB, CD, and EF are two-digit numbers, where A, B [#permalink] New post   22 Nov 2021, 12:49
Statement 1:

The units digits have to be consecutive integers.

Case 1

AB = A2

CD = C3

Would five us a units digit in the result of F = 5

A + C = 1 + 6 = 7 ——- all distinct digits

12 + 63 = 75 ———> F units digit is Prime - YES

Case 2:

AB = A4

CD = C5

Units digit of result EF ——-> F = 4 + 5 = 9

NO not prime

To ensure all digits are distinct we can make

A = 1

C = 2 ——> leading to

14 + 25 = 39

All distinct digits and the Units digit of the result = F = 9 ——NO, not prime

S1 NOT Sufficient - we have contrary answers to the yes/no question “is F Prime?”


Statement 2:

Since the result must be a 2 digit integer and we are told that C = 8

The Tens Digit of AB ——A must be = 1 ——> which means the result EF must have a Tens digit of 9

B = 2
D = 4—-> such that:

12 + 84 = 96 ——-> units digit of result = F is 6, NOT Prime

To get a contrary result and a yes answer, we can just change D to 5

AB = 12

CD = 85

12 + 85 = 97 ———> units digit of result = F is prime number 7, YES

Contrary answers to question - S2 not sufficient


Together:

From statement 2 we know we must have

AB = 1B

CD = 8D

And the tens digit of the result = E = 9

We can have no carry over from the units digit (otherwise we will not have a 2 digit result)

And

B, D must be consecutive digits

Looking at possible consecutive digit values for the units digits: B + D = F

1 + 2 = 3——> not possible because 1 is used already and each digit must be distinct

2 + 3 = 5 ——- possible, YES —> F = 5 = Prime

3 + 4 = 7 ——— possible, YES —> F = 7 = Prime

4 + 5 = 9 — not possible because the tens digit of the result = E is already 9

Any other higher consecutive digits in the Units place will result in a carryover and we will not have a 2 digit result EF, in violation of the conditions in the question.


Therefore,

C - together sufficient to tell that F = Prime and give us a definitive YES answer to the question “is the units digit of the result (i.e., F) a prime number?”

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In the problem below, AB, CD, and EF are two-digit numbers, where A, B [#permalink]
22 Nov 2021, 12:49
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Bunuel
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