Competitive Math Group3 - Grades 6-7
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Working alone, Aliyah can dig a 10 ft by 10 ft hole in six hours. One day her friend Eugene helped her and it only took 3.75 hours. How long would it take Eugene to do it alone?

Working alone, Aliyah can dig a 10 ft by 10 ft hole in six hours. One day her friend Eugene helped her and it only took 3.75 hours. How long would it take Eugene to do it alone?

1 Mark(s)

\( 11.14 \ hours \)

\( 12.91 \ hours \)

\( 11.95 \ hours \)

\( 10 \ hours \)

If the ratio between the areas of two circles is 4:1 then the ratio between their radii will be?

If the ratio between the areas of two circles is 4:1 then the ratio between their radii will be?

1 Mark(s)

1:2

2:1

1:3

4:1

How many lbs. of mixed nuts that contain \(26\%\) peanuts must Maria add to 8 lbs. of mixed nuts that contain \(64 \%\) peanuts to make a mixture with \(42 \%\) peanuts?

How many lbs. of mixed nuts that contain \(26\%\) peanuts must Maria add to 8 lbs. of mixed nuts that contain \(64 \%\) peanuts to make a mixture with \(42 \%\) peanuts?

1 Mark(s)

\( 11 \ lbs. \)

\( 18 \ lbs. \)

\( 4 \ lbs. \)

\( 17 \ lbs. \)

\(If \ x \ = \ 3t \ and \ y \ = \ \frac{(t \ + \ 1)}{2} \ and \ x \ = \ 2y \ then \ find \ the \ value \ of \ t \ ?\)

\(If \ x \ = \ 3t \ and \ y \ = \ \frac{(t \ + \ 1)}{2} \ and \ x \ = \ 2y \ then \ find \ the \ value \ of \ t \ ?\)

1 Mark(s)

1

\( \frac{2}{3} \)

\( \frac{1}{2} \)

\( \frac{1}{4} \)

How many lb of copper which costs \( \$ 3 \ /lb\) must be added to \( 6 \ lb\) of pure gold which costs \(\$ 6 \ /lb\) to make 22 carrot gold which costs \(\$ 4 \ /lb\)?

How many lb of copper which costs \( \$ 3 \ /lb\) must be added to \( 6 \ lb\) of pure gold which costs \(\$ 6 \ /lb\) to make 22 carrot gold which costs \(\$ 4 \ /lb\)?

1 Mark(s)

\( 12 \ lbs. \)

\( 19 \ lbs. \)

\( 8 \ lbs. \)

\( 13 \ lbs. \)

If one third of one fourth of a number is 15, then three tenths of that number is?

If one third of one fourth of a number is 15, then three tenths of that number is?

1 Mark(s)

35

36

45

54

If three metallic spheres of radii 6 cm, 8 cm, and 10 cm are melted to form a single sphere, then the diameter of the new sphere is?

If three metallic spheres of radii 6 cm, 8 cm, and 10 cm are melted to form a single sphere, then the diameter of the new sphere is?

1 Mark(s)

\( 24 \ cm \)

\( 30 \ cm \)

\( 12 \ cm \)

\( 15 \ cm \)

A card is drawn from a pack of 52 cards. The card is drawn at random. What is the probability that it is a spade?

A card is drawn from a pack of 52 cards. The card is drawn at random. What is the probability that it is a spade?

1 Mark(s)

\( \frac{3}{4} \)

\( \frac{1}{2} \)

\( \frac{1}{4} \)

\( \frac{3}{5} \)

How many cubes of 10 cm edge can put in a cubical box of 1 m edge? How many cubes of 10 cm edge can put in a cubical box of 1 m edge?

1 Mark(s)

1010

10001000

1000010000

100100

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