Problem Solving

Each card in a deck has an integer written on it, and the integers
on each of the 12 cards in the deck are consecutive. In a certain
game, the number points awarded for each turn is determined by
drawing two cards and multiplying the numbers shown on the
cards. If the points awarded in three turns are 40, 72, and 60,
all of the following could be the smallest numbered card in the
deck EXCEPT:

(A) -1
(B) 0
(C) 4
(D) 5
(E) 6

didnt get this q. at all...even after reading an explanation

oa is E

Since the numbers are consecutive, if 6 were to be the minimum number the next number would be 7 and minimum product would be 6*7 = 42

But we have 40 as a product. So 6 cannot be the smallest number. E

LalaB wrote:Each card in a deck has an integer written on it, and the integers
on each of the 12 cards in the deck are consecutive. In a certain
game, the number points awarded for each turn is determined by
drawing two cards and multiplying the numbers shown on the
cards. If the points awarded in three turns are 40, 72, and 60,
all of the following could be the smallest numbered card in the
deck EXCEPT:

(A) -1
(B) 0
(C) 4
(D) 5
(E) 6

didnt get this q. at all...even after reading an explanation

oa is E

Determine the range of integers that would exist for each answer choice:

A. -1: -1 to 10
B. 0: 0 to 11
C. 4: 4 to 15
D. 5: 5 to 16
E. 6: 6 to 17

We need to be able to obtain the products 40, 72, and 60 by multiplying two numbers from these ranges. The only possibilities for 40 are 8 and 5 or 10 and 4. Neither of these is possible if 6 is the smallest number. Note that in A-D, we can get 40, 72, and 60 by multiplying (5,8); (8,9); and (6,10) respectively.

I c. I misunderstood the q. I thought that each answer choice is indeed the smallest number for 40 72 60. that is why I was stuck with number 5 ( cant find how to link it to 72. I mean 40=5*8 60=5*12 but 72 -no chances with 5). I mean these two cards do not have to be from the same 12 consecutive cards. that is why I didnt even think about the range of every answer choice.

so, according to ur solution, if we have the numbers (17*6 ;17*8; 17*10), then only E is the right answer?