Is the tallest child in class A taller than the tallest child in class

Unfortunately, it's difficult to answer your question in any kind of satisfying way.
If neither statement alone is sufficient, and there's no algebraic approach available, then your goal is to find two different scenarios that satisfy both statements yet yield different answers to the target question.
If you're able to find cases that yield different answers to the target question, then you're done (the correct answer is E).
If you're unable to find such cases, the correct answer may be C or E (since it's possible you might have just missed identifying cases that yield different answers to the target question).
Unfortunately, there's no algorithmic approach to doing this.
Each question will present its own unique set of challenges.

Is the tallest child in Class A taller than tallest child in Class B?

1) The range of the heights of the children in Class A is greater than the range of the heights of the children in class B.
2) The shortest child in Class A is shorter than the shortest child in Class B.

statement 1: don't tell us anything about tallest child. Range can be higher if class A has shorter children than class B, and class B has narrow range of height children. Insufficient
Statement 2 : No information about taller child or total children or class size : Insufficient

Combined : Statement 2 contemplate statement 1 strengthening it that range is higher, but still it doesn't tell if taller are tallest than Class B or not.
Possible case : Class A high range ,Shorter and taller than Class B : Or High range shorter than class B and NOT taller than class B, Class B having mid sized range to tall height children.

Insufficient to conclude :
Answer E

1) The range of the heights of the children in Class A is greater than the range of the heights of the children in class B.
- The range is greater, but may not end with the tallest child

2) The shortest child in Class A is shorter than the shortest child in Class B.
- Does not address the questions

Combined - We do not have a starting point for the range.

E

Pretty much every answer here is bad; so, I'll do my best.

1:
Class A range: 1-20 ==>19
Class B range: 2-20 ==> 18
Notice, here the range in A is greater than the range in B BUT the tallest kid in A is not taller than the tallest kid in B.

Class A range: 1-21 ==> 20
Class B range: 2-20 ==> 18
Notice, here the range in A is greater than the range in B AND the tallest kid in A is taller than the tallest kid in B.

insuff

2:
On the GMAT, do not spend too much time thinking through this. This talks about the shortest kid and does not mention anything about the tallest kid, it cannot answer your target question alone.
insuff

1 & 2 together:
Class A range: 1-20 ==>19
Class B range: 2-20 ==> 18
Notice, here the range in A is greater than the range in B and the shortest kid in A is shorter than the shortest kid in B, BUT the tallest kid in A is not taller than the tallest kid in B.

Class A range: 1-21 ==> 20
Class B range: 2-20 ==> 18
Notice, here the range in A is greater than the range in B and the shortest kid in A is shorter than the shortest kid in B, AND the tallest kid in A is taller than the tallest kid in B.

Insuff.

1) Not sufficient. They don’t tell us if the range is higher or lower on the number line.
2) Not sufficient.
Together: Still not sufficient. It does not tell us if the difference in height btwn the shortest in the two classes is bigger than the difference in the range. Information is not sufficient to compare the potential difference in the 2 tallest children in each class.
E

HI Brent. I always get such type of questions wrong, where i miss testing one odd possibility. Such question types are also common in inequality questions.
How to tackle such problems? where testing cases is the only option and there exists no algebraic approach.
Further more in problems where it comes to choosing between C and E. Is there any algorithm kind of a thing to choose between C and E? Kindly help me.

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