The cookies in a jar contain a total of 1000 chocolate chips. All but one of these cookies contains the same number of chips; it contains one more chip than the others. The number of cookies in the jar is between one dozen and three dozen. What is the sum of the number of cookies in the jar and the number of chips in the cookie with the extra chocolate chip? (Hint: using factorization) (A) 65 (B) 64 (C) 63 (D) 66 (E) 67

65

Step-by-step explanation:

From the given information:

Let consider p to be the total numbers of the cookies

If there are 1000 chocolate chips in the jar;

The number of chocolate chips if we remove one chocolate chips = 1000 -1

= 999

The number of available choco chips on each cookie except for the one having an extra chocolate chip = 999/p

Thus, to achieve a whole number, p is required to be a factor of 999

By factorization of 999, we get:

36 > p > 12;  Thus, the value for "p" lies between 36 and 12, and which must be by 999 is 27

Thus, the number of cookies in the jar "p"= 27

However, the number of chocolate chips on with the extra chocolate chip

= 999/p + 1

= 999/27 + 1

= 37 + 1

= 38

Thus, the sum of the number of cookies in the jar +  the number of chocolate chips on with the extra chocolate chip

= 27 + 38

= 65

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step-by-step explanation:

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