A carpentry shop uses powdered wood for manufacturing furniture.

Question

A carpentry shop uses powdered wood for manufacturing furniture. The shop requires 100 pounds of powdered wood to make a table and 25 pounds to make a chair. Was the total amount of powdered wood used to make tables and chairs last week more than 20,000 pounds?

(1) The total number of tables and chairs made last week was greater than 800.
(2) The number of tables made last week was greater than the number of chairs made last week.

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ravi1522 · Answer

A carpentry shop uses powdered wood for manufacturing furniture. The shop requires 100 pounds of powdered wood to make a table and 25 pounds to make a chair. Was the total amount of powdered wood used to make tables and chairs last week more than 20,000 pounds?

(1) The total number of tables and chairs made last week was greater than 800.
(2) The number of tables made last week was greater than the number of chairs made last week.

Statement 1
The total number of tables and chairs made last week was greater than 800.

Lets take situation where it is all chairs then the wood powder required will be 800*25=20000 
so we are given that it is greater than 800 so it will be more than 20000 even if we take chairs and table both the value will be obiviously greater than 20000

Sufficient

Statement 2

(2) The number of tables made last week was greater than the number of chairs made last week.

not sufficient as we can't say about total no .

Hence Option A is correct

nemoexplicabo · Answer

Let T represent the number of tables and C represent the number of chairs produced last week. Each table requires 100 pounds of powdered wood and each chair requires 25 pounds. The total pounds of wood used is 100T + 25C, which factors as 25(4T + C). The question “Was the total amount of powdered wood used to make tables and chairs last week more than 20{,}000 pounds?” becomes an inequality: 25(4T + C) > 20{,}000, or equivalently 4T + C > 800. 
 Consider statement (1): the total number of tables and chairs made last week was greater than 800. Algebraically this means T + C > 800. To compare this to our target expression 4T + C, rewrite 4T + C as (T + C) + 3T. Because T represents a number of tables, it cannot be negative; hence 3T is always non‐negative. If T + C > 800, then (T + C) + 3T > 800 as well. In other words, statement (1) forces 4T + C to exceed 800, which guarantees that more than 20{,}000 pounds of wood were used. Statement (1) alone is sufficient. 
 Consider statement (2): the number of tables made was greater than the number of chairs made, i.e., T > C. This tells us the composition of production but not the scale. We can find values consistent with this statement that satisfy and that do not satisfy 4T + C > 800. For instance, if T = 1 and C = 0 then 4T + C = 4, which is not greater than 800, so the answer to the question would be “no.” If T = 401 and C = 400, then T > C is still true, and 4T + C = 4×401 + 400 = 2004 > 800, so the answer is “yes.” Because both “yes” and “no” are possible, statement (2) alone is insufficient.  
 Key concept:  This is a Data Sufficiency inequality question. The trick is to translate the word problem into an algebraic inequality and manipulate the expressions so that you can compare them to what the statements give you.
 Common trap:  Many students look at statement (1) and think “T + C > 800 doesn’t tell me anything about 4T + C,” or they try plugging numbers randomly without rewriting 4T + C in a useful way. The trap is not recognizing that 4T + C = (T + C) + 3T, which shows that any positive number of tables only increases the sum beyond the threshold.
 Takeaway:  In Data Sufficiency problems involving word problems and inequalities, reduce everything to algebra and look for ways to rewrite the target expression in terms of the quantities provided by the statements.

Edskore · Answer

This is a Data Sufficiency question testing inequalities with weighted sums — one of the sneakier DS patterns because it looks like you need exact numbers when you really don't.

First, let's set up the question. Let T = tables and C = chairs made last week. Total wood = 100T + 25C. We need to know: is 100T + 25C > 20,000? Dividing everything by 25, this simplifies to: is 4T + C > 800?

Statement 1: T + C > 800

Here's the key insight. We need 4T + C > 800, and we know T + C > 800. Rewrite our target: 4T + C = (T + C) + 3T. Since T represents a count of tables, T >= 0, so 3T >= 0. That means 4T + C = (T + C) + 3T >= (T + C) > 800. Done — the answer to the question is always YES.

Statement 1 is sufficient.

Statement 2: T > C

This tells us about the ratio of tables to chairs but nothing about the total quantity. If T = 1 and C = 0, total wood = 100 (not > 20,000). If T = 201 and C = 0, total wood = 20,100 (yes > 20,000). We can get both YES and NO answers.

Statement 2 is not sufficient.

Answer: (A)

Common trap:  The mistake I see most often on this type is jumping into testing specific numbers for Statement 1 without first simplifying the algebra. Students try cases like "what if 500 tables and 301 chairs" and end up spending 3 minutes on something you can prove in 30 seconds with the inequality relationship. In DS, always ask: can I compare the given information directly to what I need, without finding exact values?

Takeaway:  When a DS question asks about a weighted sum and gives you information about an unweighted sum, check whether the weights being >= 1 (or all positive) automatically make the weighted version larger — that one-line comparison can save you a ton of time.

ExpertsGlobal5 · Answer

Explanation:  
   
Let the number of tables manufactured last week be T.
Let the number of chairs manufactured last week be C.
Since the shop requires 100 pounds of powdered wood to make a table and 25 pounds to make a chair:
The total amount of powdered wood used last week = 100T + 25C.
  We need to find whether 100T + 25C > 20,000.  
 
 Statement (1) 
 
T + C > 800 
The minimum possible amount of powdered wood used that satisfies the given condition will be obtained when T = 0 and C = 801.
The   minimum amount of powdered wood used   = 100T + 25C =   100(0) + 25(801) = 20,025 > 20,000  .
 
It is possible to determine that 100T + 25C > 20,000.   Hence, Statement (1) is sufficient   . 
 
 Statement (2) 
 
T > C 
 Possibility 1:  If T = 10 and C = 1  , then 100T + 25C = 100(10) + 25(1) =   1,025 < 20,000  .
 Possibility 2:    If T = 1000 and C = 1  , then 100T + 25C = 100(1000) + 25(1) =   100,025 > 20,000  .
 
It is NOT possible to determine whether 100T + 25C > 20,000.   Hence, Statement (2) is insufficient   . 
 
  A is the correct answer choice.

A carpentry shop uses powdered wood for manufacturing furniture.

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GMAT Data Sufficiency (DS) Questions

A carpentry shop uses powdered wood for manufacturing furniture.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

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