ISEE sample questions, with worked answers

D: shy. A timid person lacks confidence and is easily frightened: shy.

C: out of date. Obsolete things are no longer used because something newer replaced them: out of date.

D: quiet. "Unlike her talkative brother" signals a contrast, and "rarely spoke" confirms it: quiet.

A: contradictory. Safe versus needing urgent repairs: the reports were contradictory. Identical is the opposite.

A: orderly and step by step. Methodical means doing things in a careful, planned order: orderly and step by step. A methodical person may also be slow, but slowness is not what the word means.

1. Put the word in a sentence: "He was methodical about packing, one list at a time."
2. Try each choice in its place: "orderly and step by step about packing" keeps the sense.
3. None of the others fits someone working through a list in order.

The trap: Picking a choice that often goes with the word (a careful person can be slow or shy) instead of the one that means the same thing.

A: helpful. Beneficial means having a good effect: helpful. The root "bene" (well, good) is the same as in benefit and benefactor.

1. Look for a word part you know: "bene," as in benefit.
2. A benefit is something good, so beneficial describes something that does good.
3. Helpful is the only choice about a good effect; harmful is its opposite.

The trap: Guessing from the sound of the word. Roots are more reliable than sound on the harder synonyms near the end of the block.

A: reserved. "But" sets up a contrast with "chatting with everyone." The blank needs the opposite of chatty: reserved, meaning quiet and holding back.

1. Find the clue word: "but" means the two halves contrast.
2. The second half says she became chatty.
3. So at first she was the opposite: reserved.

The trap: Choosing "talkative," which matches the second half of the sentence instead of contrasting with it.

A: unsafe. "Because" means the blank gives the reason for closing the bridge until it is repaired. Only a problem that repair fixes works: unsafe.

1. Find the clue: "because" links a cause to the closing.
2. Repairs fix damage, so the cause is a problem with the bridge itself.
3. Unsafe is the only choice repairs would fix.

The trap: Choosing "crowded," which could explain a closing but would not need engineers to repair anything.

C: n + 2. Test with even numbers such as 2 and 4: 2 + 2 = 4 and 4 + 2 = 6, both even. The rule behind it: even + odd is odd, even + even is even, and even × anything is even. Each other choice is odd for at least one even n.

B: 36 cm. The row is 5 × 3 = 15 cm long and 3 cm tall. Its perimeter is 2 × (15 + 3) = 36 cm. Adding all the squares' perimeters (60 cm) counts the shared sides, which are inside the shape.

A: The quantity in Column A is greater.. The third angle is 180° − 32° − 62° = 86°. It is greater than 60°.

D: The relationship cannot be determined from the information given.. If x = 2, both columns are 4, so they are equal. If x = 3, Column A is 9 and Column B is 6, so A is greater. Different allowed values give different answers, so the relationship cannot be determined.

1. Try the smallest allowed value, x = 2: A = 4, B = 4, equal.
2. Try x = 3: A = 9, B = 6, A is greater.
3. Two different results, so the answer is "cannot be determined."

The trap: Trying only one number. On a comparison with a letter, always try at least two allowed values, including the smallest.

C: The two quantities are equal.. 30% of 50 is 0.3 × 50 = 15, and 50% of 30 is 0.5 × 30 = 15. They are equal. (a% of b always equals b% of a.)

1. Column A: 0.3 × 50 = 15.
2. Column B: 0.5 × 30 = 15.
3. Both are 15, so the quantities are equal.

The trap: Assuming the column with the bigger number (50%) must be bigger. Work both out: it takes ten seconds.

A: 12. 8 cups of milk is 4 times the 2 cups in the recipe, so the flour is 4 times 3 cups: 12 cups.

1. How many times bigger is the milk? 8 ÷ 2 = 4.
2. Scale the flour the same way: 3 × 4 = 12.
3. Check the ratio: 12 to 8 is 3 to 2.

The trap: Adding instead of scaling: 8 is 6 more than 2, and 3 + 6 = 9. Ratios multiply.

C: Louis Braille turned a complicated military code into a practical reading system for blind people.. The passage follows Louis from his injury to inventing and spreading his six-dot system. The injury is only the starting point, and the army's "night writing" was a code for soldiers, not a reading system.

A: Tracing each letter took so long that readers lost track of the sentence.. The second paragraph says tracing each letter "took so long that a reader could forget the beginning of a sentence before reaching its end."

D: read messages without using a light.. The third paragraph says it let messages "be read in the dark without a light that might give away a position."

A: how a routine record became valuable in a way no one expected. The first paragraph describes the plain, repetitive log; the second and third explain that this sameness now makes it useful to historians. The whole passage is about that unexpected value.

1. Say each paragraph in a few words: a dull daily log; now a treasure for historians; the keepers never imagined it.
2. Put them together: an ordinary record that turned out to be valuable.
3. Only the first choice covers all three paragraphs.

The trap: Choosing "storms," which appears in one sentence. A main-idea answer has to fit the whole passage.

A: they were kept the same way, in the same place, for many years. The second paragraph gives the reason: "Because the entries were made in the same place, in the same way, for so many years," they form a long, unbroken record.

1. Find the word "because" in paragraph 2.
2. It gives the reason: same place, same way, many years.
3. The third choice is contradicted in paragraph 3, and the fourth in paragraph 1.

The trap: Choosing an answer the passage contradicts. Each wrong choice here is ruled out by a specific line.

B: 12. Brackets first: 6 − 3 = 3. Then the exponent: 3² = 9. Then multiply and divide from left to right: 2 × 9 = 18, and 18 ÷ 2 = 9. Last, add: 3 + 9 = 12. Adding 3 + 2 first gives 22.5.

C: 24 units. a² + b² = c², so the missing leg² = 25² − 7² = 625 − 49 = 576, and the leg is √576 = 24. Subtracting the lengths (25 − 7 = 18) skips the squares.

A: 2. Dividing by a fraction is multiplying by its reciprocal: 3/5 × 10/3 = 30/15 = 2.

1. Flip the second fraction: 3/10 becomes 10/3.
2. Multiply: 3/5 × 10/3 = 30/15.
3. Simplify: 30/15 = 2.

The trap: Multiplying the fractions as written (9/50), which answers a different question.

A: 54 square cm. Length plus width is half the perimeter: 30 ÷ 2 = 15, so the width is 15 − 9 = 6 cm. The area is 9 × 6 = 54 square cm.

1. Half the perimeter is one length plus one width: 15 cm.
2. Width = 15 − 9 = 6 cm.
3. Area = 9 × 6 = 54 square cm.

The trap: Subtracting the length from the whole perimeter (30 − 9 = 21), forgetting that the perimeter counts each side twice.

A: 20. Four numbers with a mean of 15 add up to 4 × 15 = 60. The three known numbers add up to 40, so the fourth is 60 − 40 = 20.

1. Total = mean × count = 15 × 4 = 60.
2. Known numbers: 12 + 18 + 10 = 40.
3. Fourth number: 60 − 40 = 20.

The trap: Taking the mean of the three known numbers (about 13), which ignores that the four must average 15.