@eagleeye....I found the explanation in the Princeton website like this :
A. Yes. Since the average of the five numbers is 5, their sum is 25. For statement (1), if exactly three of the integers are consecutive primes, then the only possibilities for the primes are (2, 3, 5) or (3, 5, 7). Neither of these sets of numbers has an average of 4, so at least one prime must be discarded. Now, try excluding numbers and working with the averages. For example, in the only case that works, exclude the 7 from the set of (X, Y, 3, 5, 7). So X = 4 so that when we remove Y the average of the three remaining numbers is 4. Finally, the fifth number Y must then be 6 so that the sum of all five of the numbers is 25 - (3, 4, 5, 6, 7). In all other cases, the required numbers are either not single digit, not distinct or give a fourth prime. Hence, AD. Statement (2) is insufficient information to determine all the numbers. The correct answer is A.
B. No. Since the average of the five numbers is 5, their sum is 25. For statement (1), if exactly three of the integers are consecutive primes, then the only possibilities for the primes are (2, 3, 5) or (3, 5, 7). Neither of thesesets of numbers has an average of 4, so at least one prime must be discarded. Now, try excluding numbers and working with the averages. For example, in the only case that works, exclude the 7 from the set of (X, Y, 3, 5, 7). So X = 4 so that when we remove Y the average of the three remaining numbers is 4. Finally, the fifth number Y must then be 6 so that the sum of all five of the numbers is 25 - (3, 4, 5, 6, 7). In all other cases, the required numbers are either not single digit, not distinct or give a fourth prime. Hence, AD. Statement (2) is insufficient information to determine all the numbers. The correct answer is A.
C. No. Since the average of the five numbers is 5, their sum is 25. For statement (1), if exactly three of the integers are consecutive primes, then the only possibilities for the primes are (2, 3, 5) or (3, 5, 7). Neither of these sets of numbers has an average of 4, so at least one prime must be discarded. Now, try excluding numbers and working with the averages. For example, in the only case that works, exclude the 7 from the set of (X, Y, 3, 5, 7). So X = 4 so that when we remove Y the average of the three remaining numbers is 4. Finally, the fifth number Y must then be 6 so that the sum of all five of the numbers is 25 - (3, 4, 5, 6, 7). In all other cases, the required numbers are either not single digit, not distinct or give a fourth prime. Hence, AD. Statement (2) is insufficient information to determine all the numbers. The correct answer is A.
D. No. Since the average of the five numbers is 5, their sum is 25. For statement (1), if exactly three of the integers are consecutive primes, then the only possibilities for the primes are (2, 3, 5) or (3, 5, 7). Neither of these sets of numbers has an average of 4, so at least one prime must be discarded. Now, try excluding numbers and working with the averages. For example, in the only case that works, exclude the 7 from the set of (X, Y, 3, 5, 7). So X = 4 so that when we remove Y the average of the three remaining numbers is 4. Finally, the fifth number Y must then be 6 so that the sum of all five of the numbers is 25 - (3, 4, 5, 6, 7). In all other cases, the required numbers are either not single digit, not distinct or give a fourth prime. Hence, AD. Statement (2) is insufficient information to determine all the numbers. The correct answer is A.
E. No. Since the average of the five numbers is 5, their sum is 25. For statement (1), if exactly three of the integers are consecutive primes, then the only possibilities for the primes are (2, 3, 5) or (3, 5, 7). Neither of these sets of numbers has an average of 4, so at least one prime must be discarded. Now, try excluding numbers and working with the averages. For example, in the only case that works, exclude the 7 from the set of (X, Y, 3, 5, 7). So X = 4 so that when we remove Y the average of the three remaining numbers is 4. Finally, the fifth number Y must then be 6 so that the sum of all five of the numbers is 25 - (3, 4, 5, 6, 7). In all other cases, the required numbers are either not single digit, not distinct or give a fourth prime. Hence, AD. Statement (2) is insufficient information to determine all the numbers. The correct answer is A.
Now i am more confused, Can anyone clarify the doubt?
eagleeye wrote:Hi karthikpandian19:
I got the answer as
B. Let me explain:
We are given that:
Average of 5 distinct single digit integers is 5. First off for single digit integers, I assume single digit refers to them being positive, correct me if I am wrong. Then we have 0,1,2,3,4,5,6,7,8,9 as the set to choose from. Let the integer digits be a,b,c,d,e where all are distinct.
Now we have (a+b+c+d+e)/5 = 5 then a+b+c+d+e = 5*5 = 25.
We are also told that when two are removed average of the rest is 4. Let the removed ones be a and b. Then (c+d+e)/3 = 4 or c+d+e = 12.
Then from these two we get that a+b = 13. Since sum of a and b is greater than the sum of c,d,e the largest number must be among a,b.
Now since the digits are distinct, a+b combination can be
a. 9+4
b. 8+5
c. 7+6
Hence from the options we have to check which of 7,8,9 is the greatest.
1) We have 3 of the integers as consecutive primes. From our set of 0 to 9, those 3 can either be,
a. 2,3,5 or
b. 3,5,7
Case 1a) 2,3,5: if this is the case, since 2+3+5 = 10; the other two numbers must equal 25-10 = 15, which means they can be either 9+6 or 8+7. clearly we can't find the largest from this information.
2a) 3,5,7 : we can do similar analysis, but it isn't necessary. since we already know that the information is insufficient.
2) We are given that smallest integer is 3, since
our original groups (a+b) were:
a. 9+4
b. 8+5
c. 7+6
with no 3 as an option, we must have that 3 belongs to one of the numbers of c,d,e. let 3 = c, then c+d+e=12 => d+e = 12- c = 12-3 = 9.
d+e = 9, therefore we can have only 4,5 are the option for 4+5=9, since all numbers are distinct and 3 is the smallest number. therefore we have c,d,e = 3,4,5. Since 4 and 5 occur in c,d,e, this leaves only one option for a+b which is 6+7. So we get that the largest number is 7. Hence, this is sufficient and
B is the correct answer.
Let me know if I got it right and if it helps
