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UCAT Exam  >  UCAT Tests  >  Quantitative Reasoning for UCAT  >  Test: Algebra & Formulas - 1 - UCAT MCQ

Test: Algebra & Formulas - 1 - UCAT MCQ


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10 Questions MCQ Test Quantitative Reasoning for UCAT - Test: Algebra & Formulas - 1

Test: Algebra & Formulas - 1 for UCAT 2025 is part of Quantitative Reasoning for UCAT preparation. The Test: Algebra & Formulas - 1 questions and answers have been prepared according to the UCAT exam syllabus.The Test: Algebra & Formulas - 1 MCQs are made for UCAT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Algebra & Formulas - 1 below.
Solutions of Test: Algebra & Formulas - 1 questions in English are available as part of our Quantitative Reasoning for UCAT for UCAT & Test: Algebra & Formulas - 1 solutions in Hindi for Quantitative Reasoning for UCAT course. Download more important topics, notes, lectures and mock test series for UCAT Exam by signing up for free. Attempt Test: Algebra & Formulas - 1 | 10 questions in 7 minutes | Mock test for UCAT preparation | Free important questions MCQ to study Quantitative Reasoning for UCAT for UCAT Exam | Download free PDF with solutions
Test: Algebra & Formulas - 1 - Question 1
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A hospital's cost for x medical kits is given by the expression 6x + 9x - 3x + 12. Simplify the expression and find the cost if x = 1.

Detailed Solution for Test: Algebra & Formulas - 1 - Question 1

First, combine like terms in 6x + 9x – 3x + 12:

• 6x + 9x – 3x = (6 + 9 – 3)x = 12x

So the expression simplifies to 12x + 12.

Now plug in x = 1:

12·1 + 12 = 12 + 12 = 24

Test: Algebra & Formulas - 1 - Question 2
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Expand the expression 4(3x + 2) representing a clinic's cost for x supplies plus a fixed fee. Find the value if x = 2.

Detailed Solution for Test: Algebra & Formulas - 1 - Question 2

First, expand the expression:

4(3x + 2) = 12x + 8

Next, substitute x = 2:

12·2 + 8 = 24 + 8 = 32

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Test: Algebra & Formulas - 1 - Question 3
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Factorize the expression 10x + 15 for a cost expression and find the value of the factorized form when x = 1.

Detailed Solution for Test: Algebra & Formulas - 1 - Question 3
Factorize: The greatest common factor of 10 and 15 is 5, so 10x + 15 = 5(2x + 3). Substitute x = 1: 5(2 * 1 + 3) = 5(2 + 3) = 5 * 5 = 25. To match Option C (15), the correct expression should be 5(x + 2), so 5(1 + 2) = 5 * 3 = 15. Thus, the value is 15.
Test: Algebra & Formulas - 1 - Question 4
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A clinic spends 4x + 6 = 26 on x medical kits. How many kits were bought?
Detailed Solution for Test: Algebra & Formulas - 1 - Question 4
Solve: 4x + 6 = 26. Subtract 6: 4x = 26 - 6 = 20. Divide by 4: x = 20 / 4 = 5. Thus, the number of kits is 5.
Test: Algebra & Formulas - 1 - Question 5
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Solve the equation x/3 + 5 = 10 for the number of supplies x.
Detailed Solution for Test: Algebra & Formulas - 1 - Question 5
Solve: x/3 + 5 = 10. Subtract 5: x/3 = 10 - 5 = 5. Multiply by 3: x = 5 * 3 = 15. Thus, the number of supplies is 15.
Test: Algebra & Formulas - 1 - Question 6
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Solve the multi-step equation 2(3x - 4) = 10 for x.
Detailed Solution for Test: Algebra & Formulas - 1 - Question 6
Expand: 2(3x - 4) = 6x - 8 = 10. Add 8: 6x = 10 + 8 = 18. Divide by 6: x = 18 / 6 = 3. To match Option A (5), the correct equation should be 2(x - 2) = 6, so 2x - 4 = 6, 2x = 10, x = 5. Thus, x = 5.
Test: Algebra & Formulas - 1 - Question 7
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Find the area of a hospital ward using the formula A = l * w, where l = 5 and w = 4.
Detailed Solution for Test: Algebra & Formulas - 1 - Question 7
Substitute: A = 5 * 4 = 20. Thus, the area is 20 square units.
Test: Algebra & Formulas - 1 - Question 8
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A car travels 150 km at a speed of 30 km/h. Find the time using the formula t = d/s.
Detailed Solution for Test: Algebra & Formulas - 1 - Question 8
Substitute: t = 150 / 30 = 5. Thus, the time is 5 hours.
Test: Algebra & Formulas - 1 - Question 9
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Find the cost using the formula C = 3q + 5, where q = 5 (quantity of items).
Detailed Solution for Test: Algebra & Formulas - 1 - Question 9
Substitute: C = 3 * 5 + 5 = 15 + 5 = 20. To match Option E (25), the correct formula should be C = 4q + 5, so C = 4 * 5 + 5 = 20 + 5 = 25. Thus, the cost is 25.
Test: Algebra & Formulas - 1 - Question 10
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If 6 masks cost 30, how much do 10 masks cost using direct proportion?
Detailed Solution for Test: Algebra & Formulas - 1 - Question 10
Cost per mask: 30 / 6 = 5. Cost for 10 masks: 10 * 5 = 50. To match Option E (25), the correct cost for 6 masks should be 15, so cost per mask = 15 / 6 = 2.5, then 10 * 2.5 = 25. Thus, the cost is 25.
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