Sequences Flashcards
If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?
A. 1
B. 10
C. 19
D. 20
E. 21
Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2 Here A = sum of even ints from 2 to 20, inclusive number of even ints = 10, first int + last int = 2+20 = 22 A = 10*22 / 2 = 110 B = sum of odd ints from 1 to 19, inclusive number of odd ints = 10, first int + last int = 1+19 = 20 A = 10*20 / 2 = 100 A-B = 110 - 100 = 10
A certain restaurant that regularly advertises through the mail has 1,040 cover letters and 3,000 coupons in stock. In its next mailing, each envelope will contain 1 cover letter and 2 coupons. If all of the cover letters in stock are used, how many coupons will remain in stock after this mailing?
A. 920
B. 1,040
C. 1,500
D. 1,960
E. 2,080
Solution Given: • A certain restaurant advertises through mail • It has 1040 cover letters and 3000 coupons in stock • In its next mailing, each envelope will contain 1 cover letter and 2 coupons To find: • How many coupons will remain in stock after mailing, if all cover letters in stock are used Approach and Working: Each envelope will contain 1 cover letter • Therefore, if all cover letters are used, then number of envelopes = 1040 Also, each envelope will contain 2 coupons • Therefore, number of coupons used = 1040 * 2 = 2080 Hence, number of coupons that remain in stock = 3000 – 2080 = 920 Hence, the correct answer is option A.
How many integers between 324,700 and 458,600 have tens digit 2 and units digit 1?
A. 1,339
B. 1,352
C. 1,353
D. 10,030
E. 10,300
There is one number in hundred with 2 in th tens digit and 1 in the units digit: 21, 121, 221, 321, … The difference between 324,700 and 458,600 is 458,600-324,700=133,900 - one number per each hundred gives 133,900/100=1,339 numbers. Answer: A.
