Test: Problem Solving- 3 - CUET Commerce MCQ

Step 1: Analyze the Question :- We have to make a seven-letter code, but some of our letters are repeated. We have three As two Bs, one C, and one D. We have to calculate the possible number of different codes.

Step 2: State the Task :- We'll calculate the number of permutations, remembering to take the repeated letters into account.

Step 3: Approach Strategically :- To calculate the number of permutations where some of the elements are indistinguishable, we'll divide the total number of permutations by the factorial of the number of indistinguishable elements.

So we have :- 

Step 1: Analyze the Question
We know two things about x: it's an integer, and 2.134 x 10% < 210,000. 

Step 2: State the Task
Find the greatest possible value for X. 

Step 3: Approach Strategically
To multiply a decimal quantity by 10%, move the decimal point x places to the right. For 2.134, moving the decimal point 5 places to the right results in the number 213,400. That's just over the limit of 210,000, so the maximum value of x is 4. The correct answer is (D). 

Step 4: Confirm Your Answer
A great way to confirm the answer on this type of question is to write the number down on your noteboard before counting the number of decimal places to move.

Step 1: Analyze the Question 
John spends 40% on one thing and 30% less than that on another. Since the answer choices are percents, picking 100 is a good idea. Some answer choices are widely spread out. When choices are spread out, estimation and logic are also great approaches. 

Step 2: State the Task 
What percent of last month's earnings did John have left over? We now know that we'd pick $100 as his earnings. (We care much more about picking manageable numbers than about giving imaginary people a living wage.) It's also important to focus on the fact that we are solving for what he has left after paying for rent and the dishwasher, not what he spent on those things. 

Step 3: Approach Strategically 
Some answer choices could be logically eliminated right away. After spending 40% of his earnings on rent, he'd have 60% left. Then he spends some more. Therefore, no answer 60% or greater could be possible. That eliminates (D) and (E) very quickly. And since simple combinations of percents are rarely the right answer, the odds of the right answer being “subtract 40% and then subtract 30%" are very small. That makes 100% - 40% - 30% = 30%, choice (A), a safe elimination as well. We could make a 50/50 guess very quickly on this problem, which is sometimes a good thing to do if you are falling behind pace. But let's say that you had the time to solve. Picking $100 for his earnings, we see that John spends $40 on rent. He spends 30% less than $40 on a dishwasher; “30% less than something” is the same as “90% of that something." So John spent 0.7($40), or $28, on a dishwasher. Taking $40 and $28, or $68 away from $100, John is left with $32. That's 32% of his original earnings, so choice (B) is correct. 

Step 4: Confirm Your Answer 
If you misread “30% less than his rent" as "30% of his earnings," and chosen (A) as a result, this step would save you from a wrong answer. Also, (D) is another trap answer that represents the total percentage of this earnings that John spent.

Step 1: Analyze the Question 
For this abstract number properties question, we can either apply the rules for odd and even numbers directly or simply pick some numbers to solve the question. 

Step 2: State the Task 
We must determine which answer choice must always be odd or, in other words, eliminate any answer choices that can be even. 

Step 3: Approach Strategically 
For some number properties questions, using rules (if you are certain of them) is faster than Picking Numbers. In this question, the condition that k and p are negative and are "not both even" complicates Picking Numbers but not applying rules. Since we have rules for odd and even numbers, we can apply them directly to the answer choices. We start with (E), since this is a "which of the following" question. (E): Because 2 times any value is even, 2(k + p) will always be even. Subtracting one from an even number will always result in an odd number. Therefore, (E) is always odd and must be the correct answer. 

Step 4: Confirm Your Answer
You can confirm your answer by noting that (A) through (D) could be even, judging by odd and even rules. (B) is always even, for example. (A) is odd when k and p are both odd, but the question stem allows for the possibility that one of them is even, and in such a case kp is even.

Step 1: Analyze the Question
The sentences in this word problem need to be translated into algebraic statements so that we can determine the relationship between the number of books that Peter and Nikki have read. 

Step 2: State the Task
Once the word problem has been translated, we will apply basic algebra to simplify the statement to match the correct answer choice.

Step 3: Approach Strategically
Translating the phrase "Peter read 35 more books than Nikki," we have P = N + 35.

Step 4: Confirm Your Answer
This translation directly matches (E), but be careful to check that the variables are in the correct order.

Step 1: Analyze the Question
This question tests our ability to think critically about the characteristics of remainders in division We are told that some number, m, has a remainder of 2 when divided by 5. 

Step 2: State the Task
We can use our knowledge of number properties to take a particularly strategic approach to this problem. The key will be to pick simple, permissible numbers and apply them to the problem in the question stem. 

Step 3: Approach Strategically
Ask yourself what numbers would be permissible for m. Since m has a remainder of 2 when divided by 5, m could be any number 2 greater than a multiple of 5. The simplest number to substitute for m is 7. We know that 5 goes into 7 one time with a remainder of 2. Now, apply 7 to the rest of the question stem: 3 m divided by 5. Well, 3 x 7 = 21, and 21 divided by 5 would leave a remainder of 1. That's (B). Picking Numbers is the most efficient approach to this common GMAT question type.

Step 4: Confirm Your Answer
To double-check your work, you could test any other permissible number for m: 12, 17, 22, etc. If you tried 12, you would find that 3 x 12 = 36 and 36 divided by 5 leaves a remainder of 1. This confirms that (B) is the correct choice.

Step 1: Analyze the Question
This question gives us a complicated-looking equation with one variable. The answer choices are just numbers. 

Step 2: State the Task
Our task is to solve for the value of x. 

Step 3: Approach Strategically
Since the answer choices are potential values for the variable in the equation, we could just plug those values back in to see which value makes the equation true. Backsolving is an option whenever you can manageably plug an answer choice into the question stem. Let's say that you started with (D), x = ³/₂ That makes the equation:

That's not a true statement. So we need to try other values. It's very hard to see whether you needed a larger or smaller x, so it's perfectly fine to try different answer choices. (C) is a sensible choice to test next, as it's the most manageable. It would leave you with 2 + 2 = 3 - 3, which is also false. (E) is the next most manageable. Plugging 5 in for x makes the equation

Step 4: Confirm Your Answer 
Reread the original equation, making sure you didn't make a careless error such as switching the plus and minus signs

Step 1: Analyze the Question
In this question, we are presented with a series of parts that make up the whole- in this case, the number of students in an art class. Notice that most of the whole is identified as fractions of the whole, while one part is identified as a specific quantity. We can use this to our advantage.

Step 2: State the Task
Determine the sum of the fractions in the question stem (sculptures, oil paintings, watercolors), since this makes up all but one part of the whole number of students. Subtracting this fraction from 1 will provide the fraction of the whole that is the remaining part (mosaics). Finally, we will solve for the number of students in the class. Note that this question can also be solved by Backsolving, since all of the answer choices are numbers and we can test out the answer choices to see if 10 pieces remain after calculating the number of other pieces of artwork.

Step 3: Approach Strategically
We are told that ¹/₃ of the students create sculptures, ¹/₈ create oil paintings, ¹/₂ create watercolors, and the remaining 10 pieces are mosaics. Let's assume that the total number of students in the class is x. Then the sum of the sculptures, oil paintings, and watercolors is as follows: 

(¹/₃)x + (¹/₈)x + (¹/₂)x = x(¹/₃ + ¹/₈ + ¹/₂) = x(⁸/₂₄ + ³/₂₄ + ¹²/₂₄) = x(²³/₂₄) 

So the sum of the sculptures, oil paintings, and watercolors is ²³/₂₄ of the art in the exhibit. Therefore. the remaining 10 pieces must be 1-²³/₂₄ = ¹/₂₄ of the total pieces. We can set up the equation: 

(¹/₂₄)x = 10; x= 240

Choice (C) is correct.

Step 4: Confirm Your Answer
Plug your value for x into the original equation to confirm your calculations are correct.

First, calculate the price of the laptop this year. Then, use that price to determine what the price will be next year. After a 15% decrease in price, the system would sell for 85% of $800: 0.85 x $800 = $680. If there is a 25% increase next year, the system would sell for 125% of this year's price. That would be 125% of $680: 1.25 x $680 = $850 (D).