Title: CAT 2017 QA Slot 1: Quantitative Ability Solutions
Content: Detailed Solutions for Key Questions
Here’s a structured breakdown of potential questions and solutions for CAT 2017 QA Slot 1, focusing on common topics like Data Interpretation (DI), Logical Reasoning, and Algebra.
1. Data Interpretation (DI) – Bar Graph Analysis
Question 1:
A bar graph shows the number of students (in hundreds) enrolled in three courses (A, B, C) over five years (2012–2016). Answer the following:
a) Which course had the highest enrollment in 2014?
b) What was the percentage increase in course C enrollment from 2013 to 2015?
Solution:
a) Compare the 2014 bars for A, B, and C. Assume the graph indicates Course B had the tallest bar in 2014.
Answer: Course B.
b) If 2013 enrollment for C = 200 and 2015 = 350:
[
\text{Percentage Increase} = \left(\frac{350 - 200}{200}\right) \times 100 = 75%
]
Answer: 75%.
2. Logical Reasoning – seating arrangement
Question 2:
Six people (P, Q, R, S, T, U) are seated in a row. Conditions:
P and Q are adjacent.
S is not between R and T.
U is at one end.
Question: Who is seated third from the left?
Solution:
Step 1: Place U at an end (e.g., leftmost: U _ _ _ _ _).
Step 2: P and Q must be adjacent. Possible pairs: PQ or QP.
Step 3: S cannot be between R and T. Test arrangements:
If U is first, and PQ is second-third: U P Q _ _ _
Remaining: R, S, T. Avoid S between R and T.
Valid arrangement: U P Q R S T (S is not between R and T).
Answer: Third from left = Q.
3. Algebra – Quadratic Equations
Question 3:
Solve for x:
[
(x + 3)(2x - 5) = 14
]
Solution:
Expand: (2x^2 - 5x + 6x - 15 = 14)
Simplify: (2x^2 + x - 29 = 0)
Use quadratic formula:
[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-1 \pm \sqrt{1 + 232}}{4} = \frac{-1 \pm 15.524}{4}
]
Solutions: (x = 3.63) or (x = -4.13).
4. Number Theory – Prime Factors
Question 4:
Find the number of positive integers ≤ 100 that are divisible by 2 or 3 but not by 6.
Solution:
Divisible by 2: ( \left\lfloor \frac{100}{2} \right\rfloor = 50 )
Divisible by 3: ( \left\lfloor \frac{100}{3} \right\rfloor = 33 )
Divisible by 6 (exclude): ( \left\lfloor \frac{100}{6} \right\rfloor = 16 )
Apply inclusion-exclusion:
[
(50 + 33 - 16) - 16 = 50 + 33 - 16 - 16 = 51
]
Answer: 51.
Key Tips for CAT QA:
DI: Master quick calculations (percentages, ratios) and focus on trends.
Logical Reasoning: Draw diagrams or tables to visualize constraints.
Algebra/Number Theory: Simplify equations and check for edge cases.
Let me know if you need further clarification!
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