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How much logic and question structure do these practice questions reflect compared to the OG or main exam?

Here's how our practice questions align with the logic and structure of the Official GMAT Focus Exam: GMAT-Style Precision: Our practice questions are meticulously designed to mirror the logic and structure of Official GMAT Focus questions, ensuring that students engage with problems that closely resemble those on the actual exam. Complex Problem-Solving: We emphasize the same level of complexity found in OG questions, allowing students to develop the critical reasoning and quantitative problem-solving skills. Balanced Difficulty: Our question sets are balanced to reflect both medium and hard difficulty levels, similar to the adaptive nature of the GMAT Focus, ensuring a comprehensive preparation experience. Read More

Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The regular price of each solid oak door was twice the regular price of each hollow pine?

You started by correctly identifying that the original price ratio of the hollow pine door to the solid oak door is 1:2, with prices of $40 and $80, respectively. However, the mistake happens when you try to adjust the ratio after applying the 25% discount. You calculated that the final ratio should be 1:1.75 and that this implies a new price of $70 for the solid oak door. This step is where things go wrong. Here’s why: 1. Discount Application: The problem states that Cheryl received a 25% discount on the solid oak doors. This means you should reduce the original $80 price by 25%, which gives you $60, not $70. The correct calculation is: 80 × (1 - 0.25) = 80 × 0.75 = 60 dollars So, the price after the discount is fixed at $60. 2. Incorrect Ratio Adjustment: The ratio of 1:1.75 that you used isn't necessary here. The discount simply reduces the price to $60, and we should work with that exact price. Adjusting to $70 based on the ratio leads to an incorrect total cost because it doesn’t reflect the actual 25% discount. Correct Total Price:When you use the correct discounted price of $60 for the solid oak doors, the total cost becomes:5 × 40 + 6 × 60 = 200 + 360 = 560 dollarsI hope this helps :)Read More

How many distinct four-digit numbers can be formed by the digits {1, 2, 3, 4, 5, 5, 6, 6}?

Understand the problemWe need to form four-digit numbers using the digits {1, 2, 3, 4, 5, 5, 6, 6}.Digits can be repeated as given in the set, but the numbers must be distinct. Calculate the number of permutationsTotal digits: 8We need to choose 4 out of these 8 digits. Consider repetitionsFor each selection of 4 digits, we need to consider different cases for repetitions: 1. All digits are unique 2. One digit is repeated Case 1: All digits are uniqueSelect 4 digits from {1, 2, 3, 4, 5, 6}Number of ways to select 4 out of 6 = C(6, 4) = 15Number of permutations of 4 unique digits = 4! = 24Total = 15 * 24 = 360 Case 2: One digit is repeatedChoose 3 out of {1, 2, 3, 4, 5, 6}Number of ways to select 3 out of 6 = C(6, 3) = 20Number of permutations with one repetition = 4!/2! = 12Total = 20 * 12 = 240 Sum the casesTotal distinct four-digit numbers = 360 + 240 = 600Read More

How many integer values of x satisfy the equation |x-3|+|x-5|

Understand the problemWe need to find the number of integer solutions for the inequality |x-3| + |x-5| < |x-11|. Consider the critical points 3, 5, and 11Break the inequality into cases based on these points. Case 1: x < 3|x-3| = 3-x, |x-5| = 5-x, |x-11| = 11-x3-x + 5-x < 11-x8-2x < 11-x8-2x < 11-x-2x + x < 11-8-x < 3x > -3 Case 2: 3 ≤ x < 5|x-3| = x-3, |x-5| = 5-x, |x-11| = 11-xx-3 + 5-x < 11-x2 < 11-xx < 9 Case 3: 5 ≤ x < 11|x-3| = x-3, |x-5| = x-5, |x-11| = 11-xx-3 + x-5 < 11-x2x-8 < 11-x3x < 19x < 19/3x < 6.33 Case 4: x ≥ 11|x-3| = x-3, |x-5| = x-5, |x-11| = x-11x-3 + x-5 < x-112x-8 < x-11x < -3 (No solutions) Combine the casesFrom cases 1 and 2:-3 < x < 9 From case 3:5 ≤ x < 6.33 Find integer valuesCombining the valid ranges:5 ≤ x < 9 Integer values: 5, 6, 7, 8 ConclusionThere are 4 integer values of x that satisfy the inequality.Read More

Marla is 20 years older than Angelina. In 5 years, Marla will be 3 times as old as Angelina. What will Marla’s age be in 3 years?

First, let’s define our two variables: M = Marla’s age today A = Angelina’s age today Next, we can write two equations from the information presented in the problem stem. Since Marla is 20 years older than Angelina, we have: M = A + 20 (equation 1) Since in 5 years, Marla will be 3 times as old as Angelina, we have: M + 5 = 3(A + 5) M + 5 = 3A + 15 M = 3A + 10 (equation 2) Next, from equation 1, we can substitute A + 20 for M in equation 2, and then solve for A: A + 20 = 3A + 10 10 = 2A 5 = A Finally, we see that Angelina is 5 years old. Thus, Marla is currently 5 + 20 = 25 years old. So, in 3 years, Marla will be 28 years old.Read More

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