Are the digits A and B consecutive integers?

Question

(1) A*B=72.
(2)  15\leq{A+B}\leq{19} , where A+B is a prime number.

chetan2u · Accepted Answer

Critical information  - A and B are digits.

There are only 10 digits be it in normal scenario or in GMAT. These are 0, 1, 2......8,9.

(1) A*B=72.
 A*B=72=8*9=1*72=12*6. ..  But 8*9 is the only solution that has both factors as digits. 
So A and B are 8 and 9 in any order, but we can say that A and B are consecutive.

(2)  15\leq{A+B}\leq{19} , where A+B is a prime number.
So A+B can be 17 or 19. But the maximum sum of 2 digits can be 9+9=18.
Thus A+B=17, and only possibility is 9+8.
So A and B are 8 and 9 in any order, but we can say that A and B are consecutive.

D

SandeepS030489 · Answer

Statement 1 = A*B = 72
It can be 8*9 or it can be 1*72 (not sufficient)

Statement 2: Prime number between 15 and 19 are 17 and 19; A+B can be 17 or 19 (Not sufficient)

Combined:
A+B can be 17 or 19 and A*B is 72
only 17 satisfies this condition 8*9 and 8+9 (Sufficient when statements are combined)

yashikaaggarwal · Answer

Statement 1: A*B = 72
Factors of 72 = (1*72),(2,36),(3,24),(4,18),(6,12),(8,9)
(Insufficient)

Statement 2: 15≤A+B≤19 , where A+B is a prime number.
both 17 and 19 are prime number in the given set. 
(Insufficient)

Statement 1&2: 17=8+9 also, 8*9 = 72 
(Sufficient)

IMO C

nick1816 · Answer

Since A and B are digits, they can take integral values from 0 to 9.

Statement A-  A*B=72

Since, 72/A should be less than 10, A> 7.2.

A can be 8 or 9

1. A=8; B=9
2. A=9; B=8

Consecutive in both cases

Sufficient

Statement 2-

1. A+B= 17 or 19

19 is not possible, as one of them has to be greater than 9

2. A+B =17
Only possible solution is A=9 and B=8 or A=8 and B=9

Sufficient

D

yashikaaggarwal · Answer

But its not mentioned that they are single digit number. How can one say its only 8*9?

chetan2u · Answer

When we say digits - Only 0 to 9 are possible.

If it is 23 or 35, it will be mentioned 2-digit number.
If A and B are 23 or 35 etc, it will be mentioned that A and B are integers or A and B are 2-digit numbers.

Nipungupta9081 · Answer

IMo C

Statement 1 - a*b = 72 
there can be many combinations for this so Insufficient

Statement 2 - 15≤A+B≤19 
it can betwo values 17 and 19. Inffsufficient

taking both statements 1 & 2 
17 = 8+9 
72 = 8*9

yashikaaggarwal · Answer

I guess I still need to work Hard on quant as well. Thanks for confirming.

Posted from my mobile device

Neha2404 · Answer

IMO C
Statement-1
A*B=72 
Possibile of values of A and B are 
72*1
36*2
8*9..so on
insufficient

2.Statement 2
A+B =17
Or 
A+B =19
Insufficient

3.Both
8*9=72
And
8+9=17
Sufficient

Posted from my mobile device

sampad · Answer

very bad question.

chetan2u · Answer

Can you please elaborate on why do you think so? Will help us to improve our questions.

argerniki · Answer

When you recognize the fact that A and B are  digits  and that  digits  can only range from 0 to 9, it becomes much easier:

(1) A*B = 72

The only single-digit factor-pairs of 72 are 8*9 and 9*8.
If you don't recognize it straight away, you could write down all possible pairs (1*72, 2*36,...) and will realize it at some point.
Both possibilities are cons. integers.
Every other pair has at least one double-digit factor (e.g. 6 * 12), which makes it impossible for both A and B to be digits.

Since the only possible solutions are cons. integers
 SUFF

(2)  15\leq{A+B}\leq{19} , where A+B is a prime number.

The only two primes within this range are 17 and 19
Let's how we can construct them through a sum:

19: since 9 is the highest possible digit (and if either A or B is 9), you would need to add 10, which is not a digit
Therefore, 19 is not an option

A+B needs to be 17. Let's check the possibilites, starting with A being the highest possible digit:
If A = 9, B = 8
If A = 8, B = 9
If A = 7, B = 10
You see again that the only possible digits are 9 & 8.
Every solution under/above this combination need at least a double-digit integer (>= 10)

Therefore, the only possible solution are cons. integers
 SUFF

Answer D

CEdward · Answer

This is a sneaky parameter constraint...does GMAT really make us distinguish between digits versus integers?

chetan2u · Answer

In GMAT too, digits mean 0 to 9, and integers can be anything 2-digit, 3-digit, negative or positive.
So, you should be careful when you see the word digits. There may or may not be a direct question but digit would always mean an integer from 0 to 9.

Crytiocanalyst · Answer

(1) A*B=72.
The only digits that satisfy the equation is 9,8 
Clearly sufficient

(2)  15\leq{A+B}\leq{19} , where A+B is a prime number.
9+8=17 a prime number the only one that satisfies

Therefore IMO D

Are the digits A and B consecutive integers?

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Are the digits A and B consecutive integers?

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