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Day 381: SSC CGL Quant

5 questions. Try each one first, then open its answer.

  1. Question 1

    Time and Work. Asked once: 20 Jul 2023 S3

    69
    P and Q can do a job in 24 days, Q and R can do it in 30 days, while P and R can do it in 40 days. X is four times as efficient as P, Y is half as efficient as Q, and Z is 2.5 times as efficient as R. Determine the number of days required to complete the same job if X, Y and Z work together.

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  2. Question 2

    Time, Speed and Distance. Asked once: 17 Jul 2023 S2

    56
    A, B and C run simultaneously, starting from a point, around a circular track of length 1200m, at respective speeds of 2m/s, 4m/s and 6m/s. A and B run in the same direction, while C runs in the opposite direction to the other two. After how much time will they meet for the first time?

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  3. Question 3

    Triangles. Asked once: 11 Sep 2024 S3

    58
    In ΔABC\Delta ABC, two medians AD and BE intersect at G at right angles. If AD = 12 cm and BE = 9 cm, then the length of AB is equal to:

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  4. Question 4

    Trigonometric Ratios and Identities. Asked once: 11 Sep 2024 S1

    57
    If asin⁡3X+bcos⁡3X=sin⁡Xcos⁡Xa\sin^3 X + b\cos^3 X = \sin X\cos X and asin⁡X=bcos⁡Xa\sin X = b\cos X, then find the value of a2+b2a^2 + b^2, provided that x is neither 0∘0^\circ nor 90∘90^\circ.

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  5. Question 5

    Algebraic Identities and Simplification. Asked once: 24 Jul 2023 S4

    55
    Simplify 12+2p+12+2q+12+2r\frac{1}{2 + 2p} + \frac{1}{2 + 2q} + \frac{1}{2 + 2r}, where p=xy+zp = \frac{x}{y + z}, if q=yz+xq = \frac{y}{z + x} and r=zx+yr = \frac{z}{x + y}.

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