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Tim, Tom and Jim are triplets. Their brother Carl is exactly 3 years younger. All four are having their birthdays today.
How old can the four brothers be altogether?
(A) 53
(B) 54
(C) 56
(D) 59
(E) 60

1717. Tim, Tom and Jim are triplets. Their brother Carl is exactly 33 years younger. All four are having their birthdays today.\newlineHow old can the four brothers be altogether?\newline(A) 5353\newline(B) 5454\newline(C) 5656\newline(D) 5959\newline(E) 6060

Full solution

Q. 1717. Tim, Tom and Jim are triplets. Their brother Carl is exactly 33 years younger. All four are having their birthdays today.\newlineHow old can the four brothers be altogether?\newline(A) 5353\newline(B) 5454\newline(C) 5656\newline(D) 5959\newline(E) 6060
  1. Denote Ages: Let's denote the age of the triplets as TT. Since Carl is exactly 33 years younger than the triplets, his age will be T3T - 3. To find the total age of all four brothers, we add the ages of the triplets and Carl together.\newlineTotal age = T+T+T+(T3)T + T + T + (T - 3)
  2. Calculate Total Age: Simplify the expression for the total age by combining like terms.\newlineTotal age = 3T+(T3)3T + (T - 3)\newlineTotal age = 4T34T - 3
  3. Check Multiple-Choice Answers: We are given multiple-choice answers, so we can check which one fits the form of 4T34T - 3. We will check each option to see if it is divisible by 44 and then subtract 33 to see if it matches the form.
  4. Check Option (A): Check option (A) 5353: 53+3=5653 + 3 = 56, which is not divisible by 44.
  5. Check Option (B): Check option (B) 5454: 54+3=5754 + 3 = 57, which is not divisible by 44.
  6. Check Option (C): Check option (C) 5656: 56+3=5956 + 3 = 59, which is not divisible by 44.
  7. Check Option (D): Check option (D) 5959: 59+3=6259 + 3 = 62, which is divisible by 44. 62/4=15.562 / 4 = 15.5, which is not an integer, so this cannot be the correct age of the triplets.
  8. Check Option (E): Check option (E) 6060: 60+3=6360 + 3 = 63, which is divisible by 44. 63/4=15.7563 / 4 = 15.75, which is not an integer, so this cannot be the correct age of the triplets.
  9. Correct Mistake: We have made a mistake in our previous steps. We need to correctly check each option by adding 33 and then seeing if the result is divisible by 44. Let's go back and correctly apply the check to each option.

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