If x, y, and z are three positive consecutive odd integers, what is th

given that x,y,z are consecutive odd integers ;
#1
x, y, and z are prime numbers.
only possible 3,5,7 sufficient
#2

x < y < z
many possible numbers
insufficient
OPTION A

x y z consecutive odd.
Statement 1 - x, y, z are prime numbers. so this means x, y, z are consecutive odd prime numbers {3, 5, 7} - sufficient
Statement 2 - Insufficient
Answer - A

A.

Given: x, y, and z are three positive consecutive odd integers
Find : x+y+z : so we do not find exact values for x,y,z till we get their sum

Statement I: x, y, and z are prime numbers:: it is given that x,y,z are consecutive odd integers and they need to be prime, hence only option is {3,5,7}
Now x,y,z can assume any values but x+y+z will always be 15

Sufficient. So A or D

Statement 2: x < y < z: Now it can be any set: {3,5,7} or {11,13,15} NOT Sufficient

Hence A

If x, y, and z are three positive consecutive odd integers, what is the value of x + y + z ?

(1) x, y, and z are prime numbers.
(2) x < y < z

(1) x,y,z can be 3,5,7 only no other consecutive odd prime numbers are present. Hence Sufficient.
(2) This only tells the order
Do we need to know the order for addition --> NO
Can we give one answer for this given order--> No
Hence Insufficient

Answer A

A

I think 3, 5, 7 are the only consecutive odd prime numbers.

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 3 variables: Let the original condition in a DS question contain 3 variables or over 3 variables. In other words, there are at least three fewer equations than variables. (2) Now, we know that each condition (1) and (2) would usually give us an equation, however, since we need at least 3 equations to match the numbers of variables and equations in the original condition, the unequal number of equations and variables should logically give us an answer E.

Although A could be an answer in a few cases, it is more likely that the answer is E.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find value of x + y + z.

=> Given that: x, y, and z are three positive consecutive odd integers.

Second and the third step of Variable Approach: From the original condition, we have 3 variables (x, y, and z). To match the number of variables with the number of equations, we need 3 equations. Since conditions (1) and (2) will provide 1 equation each, E would most likely be the answer.

Since it is a Key question[INTEGER QUESTION] check A or B as an answer

Let’s take a look at each conditions separately .

Condition(1) tells us that x, y, and z are prime numbers.

=> x, y, and z are prime numbers and they are positive consecutive odd integers. The only possible combination is 3, 5, and 7.

Therefore, x + y + z = 3 + 5 + 7 = 15

Since the answer is unique, condition(1) is sufficient by CMT 2.

Condition(2) tells us that x < y < z.

=> If x = 3 ; y = 5 and z = 7 then x < y < z and x + y + z = 15

=> But If x = 11 ; y = 13 and z = 15 then x < y < z and x + y + z = 38


Since the answer is not unique, condition(2) is not sufficient by CMT 2.


Condition (1) alone is sufficient.

So, A is the correct answer.

Answer: A

(1) If x, y, and z are three consecutive odd prime numbers, they must be 3, 5, and 7.

SUFFICIENT.

(2) \(x < y < z\)

We can have \(1 + 3 + 5\) or \(3 + 5 + 7\). INSUFFICIENT.

Why couldn't there be three consecutive odd prime numbers other than 3, 5, and 7?


Consider that three consecutive odd prime numbers are n, n+2, and n+4.

Forcefully, one of these numbers should be divisible by 3. Given that, the only possibility that all three numbers are prime is when 3 is one of the numbers.

Hence, St. (1) alone is sufficient.

A

Given: x, y, and z are three positive consecutive odd integers

Target question: What is the value of x + y + z ?

Statement 1: x, y, and z are prime numbers.
Useful property: Every third odd integer is divisible by 3.
For example: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,...

Since 3 is both prime and divisible by 3, we know that 3, 5 and 7 are the ONLY set of three consecutive odd integers that are all prime
So, the answer to the target question is x + y + z = 3 + 5 + 7 = 15
Statement 1 is SUFFICIENT

Statement 2: x < y < z
Statement 2 is clearly NOT SUFFICIENT, since x, y, and z can be ANY set of three consecutive odd integers.

Answer: A

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