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GRE · Practice Sheet 33

Sheet code: GRE-S33 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Mathematics

    For the quadratic 2x² + 1x − 7 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)
    α+β=−ba,  αβ=ca\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}
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  2. 2.
    Quantitative Aptitude

    An item is bought for $300 and sold for $450. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  3. 3.
    Mathematics

    Find the distance between the points (-3, 1) and (5, 3).

    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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  4. 4.
    Mathematics

    Find the slope of the line through (-1, 8) and (-5, -5).

    Formula:Slope of a Line
    m=y2−y1x2−x1m = \dfrac{y_2-y_1}{x_2-x_1}
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  5. 5.
    Quantitative Aptitude

    Divide $1,644 between two people in the ratio 6:6. How much does each receive?

    Formula:Sharing in a Ratio
    Share=Total×partsum of parts\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}
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  6. 6.
    Quantitative Aptitude

    Find the compound interest on $2,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  7. 7.
    Quantitative Aptitude

    A can finish a job in 9 days and B in 14 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  8. 8.
    Quantitative Aptitude

    Find the HCF and LCM of 12 and 39.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  9. 9.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  10. 10.
    Quantitative Aptitude

    A can finish a job in 7 days and B in 4 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  11. 11.
    Mathematics

    Find term number 6 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  12. 12.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  13. 13.
    Mathematics

    Find the sum of the first 22 terms of an AP with first term 1 and common difference 1.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
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  14. 14.
    Quantitative Aptitude

    The sum of the ages of two people is 55 years, and one is 9 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  15. 15.
    Mathematics

    Find term number 3 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  16. 16.
    Mathematics

    Find the sum of the first 3 terms of a GP with first term 5 and common ratio 2.

    Formula:GP Sum of n Terms
    Sn=a rn−1r−1S_n = a\,\dfrac{r^{n}-1}{r-1}
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  17. 17.
    Quantitative Aptitude

    An item is bought for $900 and sold for $1,170. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  18. 18.
    Quantitative Aptitude

    A vehicle covers 237 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  19. 19.
    Quantitative Aptitude

    Find the HCF and LCM of 36 and 32.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  20. 20.
    Mathematics

    For the quadratic 5x² − 2x + 5 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)
    α+β=−ba,  αβ=ca\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}
    View formula →

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