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GRE · Practice Sheet 26

Sheet code: GRE-S26 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Quantitative Aptitude

    Two varieties costing $21 and $92 per kg are mixed to give a mixture worth $33 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)
    q1q2=p2−mm−p1\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}
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  2. 2.
    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation
    log⁡b(bk)=k\log_{b}(b^{k}) = k
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  3. 3.
    Mathematics

    Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

    Formula:Binomial Coefficient
    (nr)=n!r! (n−r)!\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}
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  4. 4.
    Quantitative Aptitude

    Find the average of these 10 numbers: 53, 83, 46, 78, 83, 89, 81, 78, 20, 59.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  5. 5.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  6. 6.
    Quantitative Aptitude

    Find the simple interest on $38,000 at 5% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  7. 7.
    Quantitative Aptitude

    Find the average of these 6 numbers: 50, 67, 48, 57, 31, 37.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  8. 8.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  9. 9.
    Mathematics

    Find the distance between the points (-7, -7) and (-4, -2).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
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  10. 10.
    Mathematics

    Find the slope of the line through (1, 8) and (-6, -2).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  11. 11.
    Quantitative Aptitude

    Find the average of these 5 numbers: 63, 22, 45, 38, 34.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  12. 12.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  13. 13.
    Mathematics

    In an arithmetic progression with first term 13 and common difference 3, find term number 6.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  14. 14.
    Mathematics

    Find the distance between the points (-4, 1) and (-2, 2).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
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  15. 15.
    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  16. 16.
    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  17. 17.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  18. 18.
    Quantitative Aptitude

    Find the average of these 10 numbers: 50, 20, 62, 49, 41, 54, 61, 32, 40, 86.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  19. 19.
    Mathematics

    In an arithmetic progression with first term 9 and common difference 8, find term number 9.

    Formula:AP nth Term
    an=a+(n−1)da_n = a + (n-1)d
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  20. 20.
    Quantitative Aptitude

    The marked price of an item is $300. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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