Quick Logic: Data Sufficiency Problem Solving Quiz Quiz

Challenge your reasoning skills with this Data Sufficiency Logical Problem Solving Quiz. Evaluate statements and determine if the provided information is enough to answer each logical question with confidence.

1. Identifying Sufficient Information

   Given that Tony has more apples than Sarah, and Sarah has more than Tom, is it sufficient to determine who has the most apples?

   1. Yes, if the number of apples is known
   2. Yes, the statements are sufficient
   3. No, the statements are insufficient
   4. Only if Sarah has more than Tony

   Explanation: The information states Tony u003E Sarah u003E Tom, so Tony has the most apples. The number is not needed for the rank order. 'No, the statements are insufficient' is incorrect since it does provide enough. The third option is misleading because knowing exact numbers is unnecessary. The last option is false and even contradicts the given statements.

2. Determining a Unique Solution

   If a number x is odd, and x + 3 is even, is this information sufficient to determine if x is divisible by 2?

   1. Yes, x is divisible by 2
   2. Only if x is greater than 10
   3. Insufficient information
   4. No, x is not divisible by 2

   Explanation: Since x is odd, it cannot be divisible by 2. The statement 'Yes, x is divisible by 2' contradicts this. There's no need to know if x is greater than 10; that doesn't affect divisibility. 'Insufficient information' is incorrect, as the parity alone provides sufficiency.

3. Comparing Heights

   Maria is taller than John, and John is taller than Emma. Is this information sufficient to determine if Maria is taller than Emma?

   1. Only if all three are the same height
   2. Not unless Emma is taller than Maria
   3. Yes
   4. No

   Explanation: The ordering implies Maria u003E John u003E Emma, so Maria is definitely taller than Emma. 'No' is incorrect as the logical sequence is clear. The same height scenario does not match with the 'taller' relationships given. The final option contradicts the provided order.

4. Evaluating Sufficiency for a Calculation

   If Sarah has x candies and Paul has double that amount, is the information sufficient to find how many more candies Paul has than Sarah?

   1. No, because x is unknown
   2. Yes, the difference is equal to x
   3. Only if Sarah has 10 candies
   4. The information is insufficient

   Explanation: Paul has 2x candies, Sarah has x, so Paul has x more. The specific value of x isn't required for the difference. 'No, because x is unknown' ignores that the expression is in terms of x. The third and fourth options needlessly restrict or dismiss what is already calculable.

5. Eliminating Unnecessary Data

   Given: (1) Peter lives in New York; (2) New York is in the USA. Is the information sufficient to say Peter lives in the USA?

   1. Yes, with statement 2 alone
   2. Yes, with both statements
   3. No, not enough information
   4. Yes, with statement 1 alone

   Explanation: Only together do the statements confirm Peter's country. Statement 1 alone gives the city, but not the country. Statement 2 is a general fact, not about Peter. Saying 'not enough information' is incorrect, as combining both answers the question fully.

6. Logical Reasoning with Days of the Week

   If today is Monday and Alice will visit in three days, is the information sufficient to determine on which day Alice will visit?

   1. No, days not specified
   2. Yes, she will visit on Thursday
   3. Only if Alice visits at noon
   4. The information is incomplete

   Explanation: Counting three days ahead from Monday leads to Thursday. 'No, days not specified' is incorrect, as days are precisely listed. The third option adds irrelevant details about time. 'The information is incomplete' is not accurate because all necessary data is present.

7. Checking for Even Numbers

   Given that y is an even integer and y = 2z, is this sufficient to state that z is also an integer?

   1. No, z can be non-integer
   2. Cannot determine without knowing y
   3. Yes, z must be an integer
   4. Only if y is positive

   Explanation: If y is an even integer and divided by 2, z will always be an integer. 'No, z can be non-integer' ignores the even integer property. The sign of y has no impact, refuting the third choice. The last option is incorrect since the specific value of y is not needed.

8. Order of Operations with Limited Data

   If a + b = 10 and a = 4, is it sufficient to solve for b?

   1. Yes, b = 6
   2. Only if b is less than a
   3. No, more information needed
   4. Cannot be determined

   Explanation: Substituting a = 4 into a + b = 10 allows solving b = 6. The other answers imply uncertainty or unnecessary constraints. 'No, more information needed', 'Only if b is less than a', and 'Cannot be determined' are all incorrect due to the direct solvability.

9. Identifying Redundant Information

   Given: (1) Sam is older than Alex; (2) Alex has a twin sibling. Is this information sufficient to determine who is older between Sam and Alex's twin?

   1. No, the information is insufficient
   2. Yes, Sam is older
   3. Only if the twin is older than Alex
   4. Yes, if twin means cousin

   Explanation: Alex's twin is the same age as Alex, so Sam is older than both. 'No, the information is insufficient' is wrong because the twin's age is implied. The third option adds a condition not present, and the last option misinterprets 'twin'.

10. Simple Algebraic Relationships

    If 2p = 8, is this information sufficient to find the value of p?

    1. No, need more data
    2. Yes, p = 4
    3. Only if p is negative
    4. The equation is inconsistent

    Explanation: Dividing both sides by 2 gives p = 4. 'No, need more data' is incorrect as no other information is necessary. The sign choice is a distractor but unnecessary since 2p = 8 yields only p = 4. 'The equation is inconsistent' is false, since it solves neatly.